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  • Springer  (234)
  • American Geophysical Union
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  • 1
    Electronic Resource
    Electronic Resource
    Amenability and Phase Transition in the Ising Model (1999)
    Springer
    Journal of theoretical probability 12 (1999), S. 549-559 
    Details
    ISSN: 1572-9230
    Keywords: Ising model ; Cayley graphs ; amenability ; Markov operators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider the Ising model with external field h and coupling constant J on an infinite connected graph G with uniformly bounded degree. We prove that if G is nonamenable, then the Ising model exhibits phase transition for some h≠0 and some J〈∞. On the other hand, if G is amenable and quasi-transitive, then phase transition cannot occur for h≠0. In particular, a group is nonamenable if and only if the Ising model on one (all) of its Cayley graphs exhibits a phase transition for some h≠0 and some J〈∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021690414168
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  • 2
    Electronic Resource
    Electronic Resource
    The Ising Model with Boundaries: Integrability and Functional Relations (1998)
    Springer
    Letters in mathematical physics 46 (1998), S. 207-218 
    Details
    ISSN: 1573-0530
    Keywords: Ising model ; boundary conditions ; Boltzmann weights.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In this Letter, we analyse the boundary conditions of the planar Ising model and determine the boundary Boltzmann weights in terms of bulk Boltzmann weights. The commutativity of the transfer matrices and their functional relations are shown.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007523720496
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  • 3
    Electronic Resource
    Electronic Resource
    On the extremality of the disordered state for the Ising model on the Bethe lattice (1996)
    Springer
    Letters in mathematical physics 37 (1996), S. 137-143 
    Details
    ISSN: 1573-0530
    Keywords: 82B20 ; 82B26 ; 82B43 ; Bethe lattice ; FK representation ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give a simple proof that the limit Ising Gibbs measure with free boundary conditions on the Bethe lattice with the forward branching ratio k≥2 is extremal if and only if β is less or equal to the spin glass transition value, given by tanh(β c SG = 1/√k.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00416016
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  • 4
    Electronic Resource
    Electronic Resource
    Temperature and Pressure Dependencies of Thermal Transport Properties of Rocks: Implications for Uncertainties in Thermal Lithosphere Models and new Laboratory Measurements of High-Grade Rocks in the Central Fennoscandian Shield (1999)
    Springer
    Surveys in geophysics 20 (1999), S. 33-59 
    Details
    ISSN: 1573-0956
    Keywords: (AGI) ; heat flow ; lithosphere ; thermal conductivity ; thermal diffusivity ; models ; uncertainty
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Measurements on thermal conductivity and diffusivity as functions of temperature (up to 1150 K) and pressure (up to 1000 MPa) are presented for Archaean and Proterozoic mafic high-grade rocks metamorphosed in middle and lower crustal pressures, and situated in eastern Finland, central Fennoscandian Shield. Decrease of 12–20% in conductivity and 40–55% in diffusivity was recorded between room temperature and 1150 K, which can be considered as typical of phonon conductivity. Radiative heat transfer effects were not detected in these samples. Pressure dependencies of the samples are weak if compared to crystalline rocks in general, but relatively typical for mafic rocks. The temperature and pressure dependencies of thermal transport properties (data from literature and the present study) were applied in an uncertainty analysis of lithospheric conductive thermal modellings with random (Monte Carlo) simulations using a 4-layer model representative of shield lithosphere. Model parameters were varied according to predetermined probability functions and standard deviations were calculated for lithospheric temperature and heat flow density after 1500 independent simulations. The results suggest that the variations (uncertainties) in calculated temperature and heat flow density values due to variations in the temperature and pressure dependencies of conductivity are minor in comparison to the effects produced by typical variations in the room temperature value of conductivity, heat production rate or lower boundary condition values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1006655023894
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  • 5
    Electronic Resource
    Electronic Resource
    Thermal Transport in BPSCCO System Between 20 and 170 K (2000)
    Springer
    Journal of superconductivity 13 (2000), S. 617-621 
    Details
    ISSN: 1572-9605
    Keywords: thermal conductivity ; (Bi,Pb) 2223 pellet ; thermal conductivity peak ; phonon + electron approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Thermal conductivity of superconducting (Bi,Pb)2223 pellet in the temperature range 20–170 K is reported. Electronic contribution to thermal conductivity in the normal state is estimated to be ∼25%. Considering both phonon and phonon + electron approach, we attempted to examine the observed nature of the temperature dependence of thermal conductivity. Our analysis strongly supports the role of phonons as well as electrons in the origin of the thermal conductivity peak in the superconducting state. Some of the microscopic quantities evaluated from the best-fit parameters obtained from phonon + electron approach give reasonable values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007837220525
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  • 6
    Electronic Resource
    Electronic Resource
    Bounds for free energy derivatives using renormalization group methods (1980)
    Springer
    Journal of statistical physics 22 (1980), S. 91-96 
    Details
    ISSN: 1572-9613
    Keywords: Renormalization group ; variational principles ; convexity ; bounds on free energy and internal energy ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The free energy of a thermodynamic system is known to be a concave function of the temperature. This fact is used, together with some results due to Fisher, to deduce bounds on the internal energy of the two-dimensional Ising model, given reasonably accurate upper and lower bounds on the free energy. These free energy bounds are derived from renormalization group transformations. Unfortunately, the numerical accuracy of the bounds on the internal energy is poor. The reasons for the failure are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01007991
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  • 7
    Electronic Resource
    Electronic Resource
    Rigorous entropy-energy arguments (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 679-694 
    Details
    ISSN: 1572-9613
    Keywords: Entropy ; phase transitions ; Ising model ; plane rotor ; spin systems ; one-dimensional models ; two-dimensional models ; symmetry breaking ; Thouless effect
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a method for making rigorous various arguments which predict that certain situations are unstable because of a balance of energy vs. entropy. As applications, we give yet another proof that the two-dimensional plane rotor has no spontaneous magnetization and we make rigorous Thouless' arguments on the one-dimensional Ising model with couplingJ/n 2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01022362
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  • 8
    Electronic Resource
    Electronic Resource
    Spontaneous magnetization of randomly dilute ferromagnets (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 369-396 
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    ISSN: 1572-9613
    Keywords: Dilute ferromagnet ; random spin system ; Ising model ; spontaneous magnetization ; percolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider Ising ferromagnets on random subgraphs of the square lattice. These are obtained by independent random selections either of sites or of bonds. We assume that for each site (or, respectively, bond) the probability of being selected exceeds the critical percolation probability. Then, at sufficiently low temperatures and zero external field, spontaneous magnetization occurs. Some further related results are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010795
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  • 9
    Electronic Resource
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    Subdominant critical singularities in the bcc Ising model (1982)
    Springer
    Journal of statistical physics 27 (1982), S. 711-719 
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    ISSN: 1572-9613
    Keywords: Ising model ; critical subdominant singularities ; series analysis of critical indices ; Pade approximants and mellin transform
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract In order to analyze coalescing singularities using series expansion, a modification of the method introduced by Baker and Hunter is proposed. The Padé approximants on the Mellin transform are computed simultaneously for the initial series and its derivatives, allowing unbiased estimates for the critical parameters. The method is applied to the series generated by Nickel for various values of the spin in the bcc Ising model. We show that even with these longer series, the subdominant indices display large variation with the spin, and remain too small compared to the universal renormalization group prediction. However, the method does not detect other singularities in the temperature plane which are responsible for the observed discrepancy. Therefore the discrepancy is not significant.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013443
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  • 10
    Electronic Resource
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    Solvable models of classical lattice gases (1981)
    Springer
    Journal of statistical physics 26 (1981), S. 783-794 
    Details
    ISSN: 1572-9613
    Keywords: Lattice gas ; correlation functions ; Ising model ; Fisher-Felderhof model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study classical lattice gases at fixed temperature but variable fugacity. It is shown how the thermodynamic functions may be calculated exactly provided the Boltzmann weights are representable as principal minors of a convolution operator. We explicitly construct this operator for the cluster models of Fisher and Felderhof.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010939
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  • 11
    Electronic Resource
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    Partition function zeros for aperiodic systems (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 285-297 
    Details
    ISSN: 1572-9613
    Keywords: Ising model ; Lee-Yang zeros ; edge singularities ; nonperiodic systems ; phase transitions ; gap labeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The study of zeros of partition functions, initiated by Yang and Lee, provides an important qualitative and quantitative tool in the study of critical phenomena. This has frequently been used for periodic as well as hierarchical lattices. Here, we consider magnetic field and temperature zeros of Ising model partition functions on several aperiodic structures. In 1D, we analyze aperiodic chains obtained from substitution rules, the most prominent example being the Fibonacci chain. In 2D, we focus on the tenfold symmetric triangular tiling which allows efficient numerical treatment by means of corner transfer matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183349
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  • 12
    Electronic Resource
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    Some numerical results on the block spin transformation for the 2D Ising model at the critical point (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 731-757 
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    ISSN: 1572-9613
    Keywords: Ising model ; renormalization group ; finite-size conditions ; critical point
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the block spin transformation for the 2D Ising model at the critical temperatureT c . We consider the model with the constraint that the total spin in each block is zero. An old argument by Cassandro and Gallavotti strongly supports the Gibbsianness of the transformed measure, provided that such model has a critical temperatureT′ c lower thanT c . After describing a possible rigorous approach to the problem, we present numerical evidence that indeedT′ c 〈T c and study the Dobrushin-Shlosman uniqueness condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183686
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  • 13
    Electronic Resource
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    Comparison and disjoint-occurrence inequalities for random-cluster models (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 1311-1324 
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    ISSN: 1572-9613
    Keywords: Random-cluster model ; Ising model ; Potts model ; comparison inequality ; BK inequality ; FKG inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A principal technique for studying percolation, (ferromagnetic) Ising, Potts, and random-cluster models is the FKG inequality, which implies certain stochastic comparison inequalities for the associated probability measures. The first result of this paper is a new comparison inequality, proved using an argument developed elsewhere in order to obtain strict inequalities for critical values. As an application of this inequality, we prove that the critical pointp c (q) of the random-cluster model with cluster-weighting factorq (≥1) is strictly monotone inq. Our second result is a “BK inequality” for the disjoint occurrence of increasing events, in a weaker form than that available in percolation theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02180133
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  • 14
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    Corrections to the critical temperature in 2D Ising systems with Kac potentials (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 1131-1138 
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    ISSN: 1572-9613
    Keywords: Kac potential ; Ising model ; critical fluctuations ; Euclidean field theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider ad=2 Ising system with a Kac potential whose mean-field critical temperature is 1. Calling γ〉0 the Kac parameter, we prove that there existsc *〉0 so that the true inverse critical temperature βcr(γ) 〉 1 +by 2 log γ-1, for anyb〈c * and γ correspondingly small. We also show that if γ→0 andb→c *, suitably, then the correlation functions (normalized and rescaled) converge to those of a non-Gaussian Euclidean field theory.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183705
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  • 15
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    The computational complexity of generating random fractals (1996)
    Springer
    Journal of statistical physics 82 (1996), S. 1299-1326 
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    ISSN: 1572-9613
    Keywords: Cluster algorithms ; computational complexity ; diffusion-limited aggregation ; Ising model ; Metropolis algorithm ; P-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion-limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential; it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation, which can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183384
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  • 16
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    Two-dimensional gas of disks: Thermal conductivity (1996)
    Springer
    Journal of statistical physics 82 (1996), S. 1453-1466 
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    ISSN: 1572-9613
    Keywords: Kinetic theory ; thermal conductivity ; molecular dynamics ; hard disks ; Enskog's Theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The phenomenon of heat conduction in a two-dimensional gas ofN hard disks is studied in the hydrostatic regime by means of nonequilibrium molecular dynamics (N ranging from 100 to 8000). For systems withN≥1500 the temperature and density profiles observed are in excellent agreement with the continuous theory, but the conductivityk differs from the one derived from Enskog's theory in a systematic way. This difference seems to slowly decrease with increasing density.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02183391
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  • 17
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    Dynamic critical behavior of a Swendsen-Wang-Type algorithm for the Ashkin-Teller model (1996)
    Springer
    Journal of statistical physics 85 (1996), S. 297-361 
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    ISSN: 1572-9613
    Keywords: Ashkin-Teller model ; Ising model ; Potts model ; Monte Carlo ; dynamical critical behavior ; cluster algorithm ; Swedsen-Wang algorithm ; Li-Sokal bound ; critical slowing down ; autocorrelation time, fitting correlated data
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the dynamic critical behavior of a Swendsen-Wang-type algorithm for the Ashkin-Teller model. We find that the Li-Sokal bound on the autocorrelation time (τint.δ≥ const xC H ) holds along the self-dual curve of the symmetric Ashkin-Teller model, and is almost, but not quite sharp. The ratio τint.δ/C H appears to tend to infinity either as a logarithm or as a small power (0.05≲p≲0.12). In an appendix we discuss the problem of extracting estimates of the exponential autocorrelation time.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02174209
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  • 18
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    Absence of renormalization group pathologies near the critical temperature. Two examples (1996)
    Springer
    Journal of statistical physics 85 (1996), S. 607-637 
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    ISSN: 1572-9613
    Keywords: Ising model ; renormalization group pathologies ; Dobrushin uniqueness theorem ; completely analytic potentials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider real-space renormalization group transformations for Ising-type systems which are formally defined by $$\exp \left[ { - H'(\sigma ')} \right] = \sum\limits_\sigma {T(\sigma ,\sigma ')} \exp \left[ { - H(\sigma )} \right]$$ whereT(σ, σ′) is a probability kernel, i.e., ∑σ′ T(σ,σ′) = 1 for every configuration σ. For each choice of the block spin configuration σ′, let σ′, let μσ′ be the measure on spin configurations σ which is formally given by taking the probability of σ to be proportional toT(σ, σ′) exp[−H(σ)]. We give a condition which is sufficient to imply that the renormalized HamiltonianH′ is defined. Roughly speaking, the condition is that the collection of measures μσ′ is in the high-temperature phase uniformly in the block spin configuration σ′. The proof of this result uses methods of Olivieri and Picco. We use our theorem to prove that the first iteration of the renormalization group transformation is defined in the following two examples: decimation with spacingb = 2 on the square lattice with β 〈 1.36β c and the Kadanoff transformation with parameterp on the trian gular lattice in a subset of the β,p plane that includes values of β greater than β c .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02199358
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  • 19
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    Almost sure quasilocality fails for the random-cluster model on a tree (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 1351-1361 
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    ISSN: 1572-9613
    Keywords: Random-cluster model ; quasilocality ; almost sure quasilocality ; tree ; Gibbs measure ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the random-cluster model on a homogeneous tree, and show that the following three conditions are equivalent for a random-cluster measure: quasilocality, almost sure quasilocality, and the almost sure nonexistence of infinite clusters. As a consequence of this, we find that the plus measure for the Ising model on a tree at sufficiently low temperatures can be mapped, via a local stochastic transformation, into a measure which fails to be almost surely quasilocal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02174134
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  • 20
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    Ernst Ising—Physicist and Teacher (1997)
    Springer
    Journal of statistical physics 88 (1997), S. 991-995 
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    ISSN: 1572-9613
    Keywords: History of statistical physics ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The Ising model is one of the standard models in statistical physics. Since 1969 more than 13800 publications using this model have appeared. In 1997 Ernst Ising celebrated his 97th birthday. Some biographical notes and milestones of the development of the Ising model are given.
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    URL: http://dx.doi.org/10.1023/B:JOSS.0000015184.19421.03
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  • 21
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    Majority-Vote Cellular Automata, Ising Dynamics, and P-Completeness (1997)
    Springer
    Journal of statistical physics 88 (1997), S. 795-805 
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    ISSN: 1572-9613
    Keywords: Cellular automata ; Ising model ; voting models ; single sin-flip dynamics ; computational complexity ; parallel computation ; P-completeness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study cellular automata where the state at each site is decided by a majority vote of the sites in its neighborhood. These are equivalent, for a restricted set of initial conditions, to nonzero probability transitions in single spin-flip dynamics of the Ising model at zero temperature. We show that in three or more dimensions these systems can simulate Boolean circuits of AND and OR gates, and are therefore P-complete. That is, predicting their state t time-steps in the future is at least as hard as any other problem that takes polynomial time on a serial computer. Therefore, unless a widely believed conjecture in computer science is false, it is impossible even with parallel computation to predict majority-vote cellular automata, or zero-temperature single spin-flip Ising dynamics, qualitatively faster than by explicit simulation.
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    URL: http://dx.doi.org/10.1023/B:JOSS.0000015172.31951.7b
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  • 22
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    Finite-Volume Glauber Dynamics in a Small Magnetic Field (1998)
    Springer
    Journal of statistical physics 90 (1998), S. 1015-1035 
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    ISSN: 1572-9613
    Keywords: Ising model ; mixing conditions ; Basuev region ; boundary conditions ; Glauber dynamics ; exponential relaxation ; spectral gap
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We consider Glauber dynamics on a finite cube in d-dimensional lattice (d≥2), which is associated with basic Ising model at temperature T=1/β≪1 under a magnetic field h 〉 0. We prove that if the “effective magnetic field” is positive, then the relaxation of the Glauber dynamics in the uniform norm is exponentially fast, uniformly over the size of underlying cube. The result covers the case of the free-boundary condition with arbitrarily small positive magnetic field. This paper is a continuation of an attempt initiated earlier by Schonmann and Yoshida to shed more light on the relaxation of the finite-volume Glauber dynamics when the thermodynamic parameter (β, h) is so near the phase transition line, (β, h); β c 〈 β&h = 0, that the Dobrushin–Shlosman mixing condition is no longer available.
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    URL: http://dx.doi.org/10.1023/A:1023249608957
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  • 23
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    Cassie's Law and Concavity of Wall Tension with Respect to Disorder (2000)
    Springer
    Journal of statistical physics 98 (2000), S. 1115-1134 
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    ISSN: 1572-9613
    Keywords: Ising model ; correlation inequalities ; surface tension ; disorder
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For the semiinfinite Ising model with quenched boundary disorder, we prove concavity inequalities for the difference of wall tensions associated with the minus and plus phases. These inequalities generalize phenomenological equalitiesknown as Cassie's law.
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    URL: http://dx.doi.org/10.1023/A:1018663611669
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  • 24
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    Pattern recognition and statistical mechanics (1969)
    Springer
    Journal of statistical physics 1 (1969), S. 71-88 
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    ISSN: 1572-9613
    Keywords: Decision theory ; Ising model ; Least square estimation ; Pattern recognition ; Plasmas ; Statistical mechanics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A mathematical connection is established between classes of problems in pattern recognition and in statistical mechanics. More explicitly, the former class embraces problems arising from the decision-theoretic approach to the automatic recognition of certain properties of patterns containing many targets. The latter class contains almost all problems involving the statistical mechanics of classical systems of interacting particles. The usefulness of the mathematical connection lies in the fact that it provides a bridge for the transfer of approximation methodologies from one area to the other. As examples of such a transfer this paper presents applications of a least mean square approximation method, which is well known in pattern recognition, to two problems in classical statistical mechanics, namely, the one-dimensional Ising problem and the one-component plasma problem. These problems were chosen because their solutions are well understood (the exact solution of the one-dimensional Ising model and the solution of the one-component plasma that is exact in the low concentration limit are both very well known) and consequently they are appropriate as “test beds” for the new approximation method. The simplest nontrivial approximate trial functions were used for the calculation of the average values of certain observables and the results were in agreement with the corresponding exact results for the Ising model in the limit of high temperature and for the one-component plasma in the limit of low concentration.
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    URL: http://dx.doi.org/10.1007/BF01007242
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  • 25
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    Convergence of block spins defined by a random field (1980)
    Springer
    Journal of statistical physics 22 (1980), S. 673-684 
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    ISSN: 1572-9613
    Keywords: Block spins ; random field ; mixing random variables ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We study the asymptotic behavior of families of dependent random variables called “block spins,” which are associated with random fields arising in statistical mechanics. We give sufficient conditions for these families to converge weakly to products of independent Gaussian random variables. We also estimate the error terms involved. In addition we give some conditions which imply that the block spins can converge weakly only to families of normal or degenerate random variables. Central to our proofs is a mixing property which is weaker than strong mixing and which holds for many random fields studied in statistical mechanics. Finally we give a simple method for determining when a stationary random field does not satisfy a strong mixing property. This method implies that the two-dimensional Ising model at the critical temperature is not strong mixing, a result obtained by a different method by M. Cassandro and G. Jona-Lasinio. The method also shows that a stationary, mean-zero, positively correlated Gaussian process indexed by ℝ is not strong mixing if its covariance function decreases liket −α , 0 〈α 〈 1.
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    Cluster expansion and generalized transfer matrices for the statistical mechanics of linear chains (1981)
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    Journal of statistical physics 24 (1981), S. 555-586 
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    ISSN: 1572-9613
    Keywords: Ising model ; Heisenberg model ; transfer matrix ; cluster expansion
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    Notes: Abstract A cluster expansion of the statistical mechanical density operator for a general linear chain model with nearest-neighbor interactions is made. This expansion is then shown to lead to an expansion of a generalized transfer matrix, whose maximum eigenvalue is the per-site partition function. A number of computational features, as well as some illustrative examples, of this approach are described.
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    Field theory of the two-dimensional ising model: II. Nonlocal specific heat (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 361-366 
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    ISSN: 1572-9613
    Keywords: Ising model ; field theory ; specific heat, nonlocality ; wave number dependence ; spectral function ; analytic continuation
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    Notes: Abstract The nonlocal specific heat is calculated for the two-dimensional Ising model and found to be identical to that found by Bray for the four-dimensional model. Furthermore, it is noted that analytic continuation in terms of a spectral function provides an especially simple description of the nonlocal specific heat. From unitarity the spectral function is the rate of pair production in the Minkowski metric, and is calculated to be equal to the velocity of the outgoing particles.
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    Higher-order susceptibilities of the regular and the random Ising model on the Cayley tree. I (1981)
    Springer
    Journal of statistical physics 26 (1981), S. 665-681 
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    ISSN: 1572-9613
    Keywords: Cayley tree ; Ising model ; higher-order susceptibilities ; critical temperature ; phase transition ; random Ising model ; diluted Ising model ; critical concentration
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    Notes: Abstract Explicit expressions for the fourth-order susceptibility χ(4), the fourth derivative of thebulk free energy with respect to the external field, are given for the regular and the random-bond Ising model on the Cayley tree in the thermodynamic limit, at zero external field. The fourth-order susceptibility for the regular system diverges at temperature T c (4) = 2k B −1 J/ln{1+2/[(z−1)3/4−1]}, confirming a result obtained by Müller-Hartmann and Zittartz [Phys. Rev. Lett. 33:893 (1974)]; Herez is the coordination number of the lattice,J is the exchange integral, andk B is the Boltzmann constant. The temperatures at which χ(4) and the ordinary susceptibility χ(2) diverge are given also for the random-bond and the random-site Ising model and for diluted Ising models.
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    The Onsager formula, the fisher-hartwig conjecture, and their influence on research into Toeplitz operators (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 575-584 
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    ISSN: 1572-9613
    Keywords: Ising model ; correlation functions ; spontaneous magnetization ; Toeplitz determinants ; Szegö limit theorems ; Toeplitz operators
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    Notes: Abstract This is not primarily a paper about applications of mathematics to statistical physics, but rather a report on how a particular problem of statistical physics has resulted in an extensive mathematical theory. The problem alluded to is the computation of the spontaneous magnetizationM o (T) of the two-dimensional Ising model with nearest-neighbor interactions, whose solution for temperaturesT below the Curie pointT c was given by the famous formula of Lars Onsager in 1948. The theory grown out of this formula is the edifice of Toeplitz determinants, matrices, and operators.
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    Relaxation times in a finite Ising system with random impurities (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 893-916 
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    ISSN: 1572-9613
    Keywords: Dynamic critical phenomena ; disordered spin systems ; Ising model ; finite size ; scaling
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    Notes: Abstract Finite-size scaling effects of the Ising model with quenched random impurities are studied, focusing on critical dynamics. In contrast to the pure Ising model, disordered systems are characterized by continuous relaxation time spectra. Dynamic field theory is applied to compute the spectral densities of the magnetizationM(t) and ofM 2(t). In addition, universal cumulant ratios are calculated to second order in ε1/4, where ε=4−d andd〈4 denotes the spatial dimension.
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    Instability of renormalization-group pathologies under decimation (1995)
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    Journal of statistical physics 79 (1995), S. 25-42 
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    ISSN: 1572-9613
    Keywords: Renormalization group ; decimation ; non-Gibbsianness ; Ising model
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    Notes: Abstract We investigate the stability and instability of pathologies of renormalization group transformations for lattice spin systems under decimation. In particular we show that, even if the original renormalization group transformation gives rise to a non-Gibbsian measure, Gibbsianness may be restored by applying an extra decimation transformation. This fact is illustrated in detail for the block spin transformation applied to the Ising model. We also discuss the case of another non-Gibbsian measure with nicely decaying correlations functions which remains non-Gibbsian after arbitrary decimation.
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    sl(N) Onsager's algebra and integrability (1996)
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    Journal of statistical physics 82 (1996), S. 87-113 
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    ISSN: 1572-9613
    Keywords: Onsager's algbera ; loop algebras ; Ising model ; integrability
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    Notes: Abstract We define ansl(N) analog of Onsager's algebra through a finite set of relations that generalize the Dolan-Grady defining relations for the original Onsager's algebra. This infinite-dimensional Lie algebra is shown to be isomorphic to a fixed-point subalgebra ofsl(N) loop algebra with respect to a certain involution. As the consequence of the generalized Dolan-Grady relations a Hamiltonian linear in the generators ofsl(N) Onsager's algebra is shown to posses an infinite number of mutually commuting integrals of motion.
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    Some new results on the two-dimensional kinetic Ising model in the phase coexistence region (1996)
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    Journal of statistical physics 84 (1996), S. 655-696 
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    Keywords: Ising model ; Glauber dynamics ; relaxation time
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    Notes: Abstract We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL with open boundary conditions, in the absence of an external field and at large inverse temperature β. We prove that the gap in the spectrum of the generator restricted to the invariant subspace of functions which are even under global spin flip is much larger than the true gap. As a consequence we are able to show that there exists a new time scalet even, much smaller than the global relaxation timet rel, such that, with large probability, any initial configuration first relaxes to one of the two “phases” in a time scale of ordert even and only after a time scale of the order oft rel does it reach the final equilibrium by jumping, via a large deviation, to the opposite phase. It also follows that, with large probability, the time spent by the system during the first jump from one phase to the opposite one is much shorter than the relaxation time.
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    Equivalences of the large deviation principle for Gibbs measures and critical balance in the Ising model (1997)
    Springer
    Journal of statistical physics 86 (1997), S. 149-164 
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    Keywords: Ising model ; Gibbs measures ; large-deviation principle
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    Notes: Abstract In this paper we obtain the equivalence of the large deviation principle for Gibbs measures with and without an external field. For the Ising model, the equivalence allows us to study the result of competing influences of a positive external fieldh and a negative boundary condition in the cube (Λ(B/h) ash↘0 for variousB. We find a critical balance at a valueB 0 ofB.
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    Metastability in the Two-Dimensional Ising Model with Free Boundary Conditions (1998)
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    Journal of statistical physics 90 (1998), S. 211-226 
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    ISSN: 1572-9613
    Keywords: Ising model ; stochastic dynamics ; metastability ; nucleation
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    Notes: Abstract We investigate metastability in the two dimensional Ising model in a square with free boundary conditions at low temperatures. Starting with all spins down in a small positive magnetic field, we show that the exit from this metastable phase occurs via the nucleation of a critical droplet in one of the four corners of the system. We compute the lifetime of the metastable phase analytically in the limit T → 0, h → 0 and via Monte Carlo simulations at fixed values of T and h and find good agreement. This system models the effects of boundary domains in magnetic storage systems exiting from a metastable phase when a small external field is applied.
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    Improved Peierls Argument for High-Dimensional Ising Models (1998)
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    Journal of statistical physics 90 (1998), S. 1051-1059 
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    ISSN: 1572-9613
    Keywords: Ising model ; Peierls contour ; low-temperature expansion ; high dimension
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    Notes: Abstract We consider the low-temperature expansion for the Ising model on $$\mathbb{Z}^d ,d \geqslant 2$$ , with ferromagnetic nearest neighbor interactions in terms of Peierls contours. We prove that the expansion converges for all temperatures smaller than Cd(log d)−1, which is the correct order in d.
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    The O(n) Loop Model on the 3–12 Lattice (1998)
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    Journal of statistical physics 92 (1998), S. 1203-1208 
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    ISSN: 1572-9613
    Keywords: Loop model ; criticality ; universality ; 3–12 lattice ; self-avoiding walk ; connective constant ; Ising model
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    Notes: Abstract The partition function of the O(n) loop model on the honeycomb lattice is mapped to that of the O(n) loop model on the 3–12 lattice. Both models share the same operator content and thus critical exponents. The critical points are related via a simple transformation of variables. When n = 0 this gives the recently found exact value μ = 1.711041... for the connective constant of self-avoiding walks on the 3–12 lattice. The exact critical points are recovered for the Ising model on the 3–12 lattice and the dual asanoha lattice at n = 1.
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    On the Phase Diagram of the Random Field Ising Model on the Bethe Lattice (1998)
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    Journal of statistical physics 93 (1998), S. 33-78 
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    ISSN: 1572-9613
    Keywords: Random external field ; Ising model ; Gibbs states ; ground states ; Bethe lattice ; residual entropy ; dipole configurations ; Griffiths singularities
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    Notes: Abstract The ferromagnetic Ising model on the Bethe lattice of degree k is considered in the presence of a dichotomous external random field ξ x = ±α and the temperature T≥0. We give a description of a part of the phase diagram of this model in the T−α plane, where we are able to construct limiting Gibbs states and ground states. By comparison with the model with a constant external field we show that for all realizations ξ = {ξ x = ±α} of the external random field: (i) the Gibbs state is unique for T 〉 T c (k ≥ 2 and any α) or for α 〉 3 (k = 2 and any T); (ii) the ±-phases coexist in the domain {T 〈 T c, α ≤ H F(T)}, where T c is the critical temperature and H F(T) is the critical external field in the ferromagnetic Ising model on the Bethe lattice with a constant external field. Then we prove that for almost all ξ: (iii) the ±-phases coexist in a larger domain {T 〈 T c, α ≤H F(T) + ε(T)}, where ε(T)〉0; and (iv) the Gibbs state is unique for 3≥α≥2 at any T. We show that the residual entropy at T = 0 is positive for 3≥α≥2, and we give a constructive description of ground states, by so-called dipole configurations.
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    An Equilibrium Lattice Model of Wetting on Rough Substrates (1999)
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    Journal of statistical physics 94 (1999), S. 299-320 
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    ISSN: 1572-9613
    Keywords: wetting ; surface tension ; rough surfaces ; Wenzel's law ; semi-infinite systems ; Ising model ; cluster expansions
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    Notes: Abstract We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies Δτ(r)=τ AW(r)−τ BW(r) of the two phases behaves like Δτ(r)∼rΔτ(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos θ(r)≈r cos θ(1), which relates the contact angle θ of a sessile droplet to the roughness of the substrate
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    The Ising Model on a Quenched Ensemble of c=−5 Gravity Graphs (1999)
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    Journal of statistical physics 94 (1999), S. 321-345 
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    ISSN: 1572-9613
    Keywords: dynamical triangulations ; quenched disorder ; Ising model
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    Notes: Abstract We study with Monte Carlo methods an ensemble of c=−5 gravity graphs, generated by coupling a conformal field theory with central charge c=−5 to two-dimensional quantum gravity. We measure the fractal properties of the ensemble, such as the string susceptibility exponent γ s and the intrinsic fractal dimension d H. We find γ s=−1.5(1) and d H=3.36(4), in reasonable agreement with theoretical predictions. In addition, we study the critical behavior of an Ising model on a quenched ensemble of the c=−5 graphs and show that it agrees, within numerical accuracy, with theoretical predictions for the critical behavior of an Ising model coupled dynamically to two-dimensional quantum gravity, with a total central charge of the matter sector c=−5.
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    Statistical Entropy of a Lattice-Gas Model: Multiparticle Correlation Expansion (1999)
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    Journal of statistical physics 96 (1999), S. 135-167 
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    ISSN: 1572-9613
    Keywords: statistical entropy ; multiparticle correlations ; cumulant expansion ; lattice gases ; Ising model
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    Notes: Abstract A formula expressing the statistical entropy of a lattice-gas model as a multiparticle correlation expansion is derived in the grand-canonical and in the canonical ensembles. The differences from the analogous expansion in the continuum case are elucidated. The Ising model in one dimension is discussed as a case study.
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    Renormalization-Group Transformations Under Strong Mixing Conditions: Gibbsianness and Convergence of Renormalized Interactions (1999)
    Springer
    Journal of statistical physics 97 (1999), S. 831-915 
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    ISSN: 1572-9613
    Keywords: renormalization group ; Gibbsianness ; finite-size conditions ; complete analyticity ; strong mixing ; equivalence of ensembles ; Ising model
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    Notes: Abstract In this paper we study a renormalization-group map: the block averaging transformation applied to Gibbs measures relative to a class of finite-range lattice gases, when suitable strong mixing conditions are satisfied. Using a block decimation procedure, cluster expansion, and detailed comparison between statistical ensembles, we are able to prove Gibbsianness and convergence to a trivial (i.e., Gaussian and product) fixed point. Our results apply to the 2D standard Ising model at any temperature above the critical one and arbitrary magnetic field.
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    Universality and Conformal Invariance for the Ising Model in Domains with Boundary (2000)
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    Journal of statistical physics 98 (2000), S. 131-244 
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    Keywords: Ising model ; boundary conditions ; renormalization group ; free boson ; conformal invariance ; critical phenomena
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    Notes: Abstract The partition function with boundary conditions for various two-dimensional Ising models is examined and previously unobserved properties of nonformal invariance and universality are established numerically.
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    Monte Carlo Transition Dynamics and Variance Reduction (2000)
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    Journal of statistical physics 98 (2000), S. 321-345 
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    ISSN: 1572-9613
    Keywords: statistical mechanics ; variance reduction ; Monte Carlo algorithms ; Metropolis algorithm ; statistical estimators ; Ising model ; histogram methods ; transition probabilities
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    Notes: Abstract For Metropolis Monte Carlo simulations in statistical physics, efficient, easy- to-implement, and unbiased statistical estimators of thermodynamic properties are based on the transition dynamics. Using an Ising model example, we demonstrate (problem-specific) variance reductions compared to conventional histogram estimators. A proof of variance reduction in a microstate limit is presented.
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    A Comparison Between Broad Histogram and Multicanonical Methods (2000)
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    Journal of statistical physics 99 (2000), S. 691-705 
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    Keywords: Monte Carlo methods ; Ising model ; computational physics
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    Notes: Abstract We discuss the conceptual differences between the broad histogram (BHM) and reweighting methods in general, and particularly the so-called multicanonical (MUCA) approaches. The main difference is that BHM is based on microcanonical, fixed-energy averages which depend only on the good statistics taken inside each energy level. The detailed distribution of visits among different energy levels, determined by the particular dynamic rule one adopts, is irrelevant. Contrary to MUCA, where the results are extracted from the dynamic rule itself, within BHM any microcanonical dynamics could be adopted. As a numerical test, we have used both BHM and MUCA in order to obtain the spectral energy degeneracy of the Ising model in 4×4×4 and 32×32 lattices, for which exact results are known. We discuss why BHM gives more accurate results than MUCA, even using the same Markovian sequence of states. In addition, such an advantage increases for larger systems.
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    Several constants arising in statistical mechanics (1999)
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    Annals of combinatorics 3 (1999), S. 323-335 
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    ISSN: 0219-3094
    Keywords: 05A15 ; 05A16 ; 05B50 ; 11Y60 ; 82B20 ; 82B41 ; random lattice models ; self-avoiding walks ; polyominoes ; Ising model ; monomers ; dimers ; ice models ; hard squares ; hard hexagons ; percolation
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    Topics: Mathematics
    Notes: Abstract This is a brief survey of certain constants associated with random lattice models, including self-avoiding walks, polyominoes, the Lenz-Ising model, monomers and dimers, ice models, hard squares and hexagons, and percolation models.
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    Particularities of Heat Conduction in Nanostructures (2000)
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    Journal of nanoparticle research 2 (2000), S. 199-204 
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    ISSN: 1572-896X
    Keywords: nanoscale heat transfer ; nanoparticles ; nanowires ; phonons ; superlattices ; thermal conductivity ; thin films ; microscale effects
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    Topics: Physics , Technology
    Notes: Abstract Heat conduction in nanostructures differs significantly from that in macrostructures because the characteristic length scales associated with heat carriers, i.e., the mean free path and the wavelength, are comparable to the characteristic length of nanostructures. In this communication, particularities associated with phonon heat conduction in nanostructures, the applicability of the Fourier law, and the implications of nanoscale heat transfer effects on nanotechnology are discussed.
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    Investigation on the effective conductivities of carbon/carbon fiber composites with inhomogeneous interphase (1997)
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    Applied mathematics and mechanics 18 (1997), S. 211-220 
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    ISSN: 1573-2754
    Keywords: composite ; thermal conductivity ; inhomogeneous interphase ; Mori-Tanaka method
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    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Mathematics , Physics
    Notes: Abstract Thermal conductivities of carbon/carbon fiber composites with inhomogeneous interphase are studied in thtis paper. The inhomogeneous interphase is modeled approximately as a multilayered structure consisting of many thin layers having homogeneous properties, and close-formed solution of the effective conductivities of the composites is obtained by using the Mori-Tanaka mean-field concept.
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    Nonisothermal polymeric fluids (1996)
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    Rheologica acta 35 (1996), S. 103-109 
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    ISSN: 1435-1528
    Keywords: Transport properties ; thermal conductivity ; FENE dumbbell model ; polymer solutions ; thermal diffusion
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    Topics: Chemistry and Pharmacology , Physics
    Notes: Abstract The phase-space kinetic theory for polymeric liquid mixtures has been further developed for molecular models without internal constraints. The theory provides expressions for the mass, momentum, and energy fluxes, each of which may in general be influenced by concentration, velocity, and temperature gradients. To illustrate the use of these results, the thermal conductivity for a dilute polymer solution is derived; the FENE dumbbell model is used to describe the mechanical behavior of the polymer chains. The Hookean dumbbell results can be obtained by letting the “finite extensibility parameter” b tend to infinity.
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    Probing the Upper Critical Field of κ-(BEDT-TTF)2Cu(NCS)2 (1999)
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    Journal of superconductivity 12 (1999), S. 497-500 
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    ISSN: 1572-9605
    Keywords: Organic superconductors ; Josephson plasma ; thermal conductivity ; upper critical field
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Studies of heat conduction and microwave absorption in the vortex state of κ-(BEDT-TTF)2Cu(NCS)2 reveal some of the specific aspects of superconductivity in this system. Moreover they allow us to probe the destruction of bulk superconductivity by a magnetic field. The two set of results yield identical magnitudes for the upper critical field with a temperature dependence distinctly different from the one suggested by the onset of resistive transition.
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    Heat conduction in Ba1−xKxBiO3 (1995)
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    Journal of superconductivity 8 (1995), S. 445-448 
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    ISSN: 1572-9605
    Keywords: High-T c superconductors ; thermal conductivity ; magnetization
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract We have investigated heat conduction of single crystal Ba1−xKxBiO3 in the temperature range of 2–300 K and in a magnetic field of up to 6 Tesla. Temperature dependence of thermal conductivityκ(T) reveals the participation of both electrons and phonons with their relative contributions that depend critically on the potassium doping concentration. Crystals underdoped with potassium (samples with higherT c) exhibit a strong suppression ofκ and a glass-like temperature dependence. In contrast, those with a higher potassium content (lowerT c) show an increase as temperature decreases with a peak near 23 K. Field dependence ofκ(H) is also very sensitive to the level of potassium doping. Crystals exhibiting a large phonon contribution show an initial drop inκ(H) at low fields followed by a minimum and then a slow rise to saturation as the field increases. The initial drop is due to the additional phonon scattering by magnetic vortices as the sample enters a mixed state. The high field behavior ofκ(H), arising from a continuous break-up of Cooper pairs, exhibits scaling which suggests the presence of an unconventional superconducting gap structure in this material.
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    The field dependence of the thermal conductivity: Evidence for nodes in the gap (1995)
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    Journal of superconductivity 8 (1995), S. 449-452 
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    ISSN: 1572-9605
    Keywords: thermal conductivity ; Andreev reflection ; vortex lines ; mixed phase
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    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract The increased thermal conductivity below Tc in YBa2Cu3O7−x (YBCO) is shown to agree with the microwave electrical conductivity, affirming that increase is due to quasiparticle conduction The field dependence, particularly in the conducting plane permits us to separate phonon and quasiparticle contributions for both YBCO and Tℓ2Ba2CuO6 single crystals.
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    Ising-like field theory (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 143-152 
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    ISSN: 1572-9613
    Keywords: Ising model ; field theory model ; stability ; pressure ; ultraviolet divergence ; infrared divergence
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    Topics: Physics
    Notes: Abstract A field theory model onR 2 in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in λ of the ground state energy, as λ→0, without using the cluster expansion.
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    Analytic and numerical evidence from quantum field theory for the hyperscaling relation dv = 2Δ−γ in the d=3 ising model (1981)
    Springer
    Journal of statistical physics 25 (1981), S. 269-290 
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    ISSN: 1572-9613
    Keywords: Ising model ; hyperscaling ; relativistic ; self-interacting Boson quantum field theory ; renormalization ; Monte-Carlo calculations ; multispin coding
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    Topics: Physics
    Notes: Abstract The hyperscaling relationdv = 2Δ - γ(d=3) for the Ising model has been shown to follow from a constructive approach proposed by one of the authors (R.S.) of a relativistic theory of self-interacting Bosons in d space-time dimensions. We present evidence that the two assumptions made in this approach are valid: On a finite Euclidean (hyper-) cubical lattice in d dimensions the renormalization map from the bare to the renormalized parameters should have nonvanishing Jacobian everywhere. We show this analytically and numerically on the boundary set of the parameters. The numerical analysis involves Monte Carlo calculations in the region where the bare coupling constantg 0 is infinite, giving the Ising model. The linear sizen of the lattice (with periodic boundary conditions) was taken to be 5, 6, and 10. There we also checked the second assumption saying that the correlation length for the Ising model is a monotonic function of the temperature. We also comment on the possible numbers of zeros of the Callan-Symanzikβ function of this theory.
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    Absence of long-range order in one-dimensional spin systems (1981)
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    Journal of statistical physics 25 (1981), S. 669-678 
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    ISSN: 1572-9613
    Keywords: Ising model ; plane rotator model ; inequalities ; long-range order
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    Topics: Physics
    Notes: Abstract For a one-dimensional Ising model with interaction energy $$E\left\{ \mu \right\} = - \sum\limits_{1 \leqslant i〈 j \leqslant N} {J(j - i)} \mu _\iota \mu _j \left[ {J(k) \geqslant 0,\mu _\iota = \pm 1} \right]$$ it is proved that there is no long-range order at any temperature when $$S_N = \sum\limits_{k = 1}^N {kJ\left( k \right) = o} \left( {[\log N]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right)$$ The same result is shown to hold for the corresponding plane rotator model when $$S_N = o\left( {\left[ {{{\log N} \mathord{\left/ {\vphantom {{\log N} {\log \log N}}} \right. \kern-\nulldelimiterspace} {\log \log N}}} \right]} \right)$$
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    Local properties of an Ising model on a Cayley tree (1982)
    Springer
    Journal of statistical physics 27 (1982), S. 441-456 
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    ISSN: 1572-9613
    Keywords: Ising model ; Cayley tree ; phase transition ; iteration ; fixed point ; bifurcation ; ferromagnetic ; antiferromagnetic.
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    Topics: Physics
    Notes: Abstract The Ising model on a Cayley tree displays a peculiar (continuous order) phase transition with zero long-range order at all finite temperatures. When one studies expection values of spins far removed from the surface (which contains a finite fraction of the total number of spins in the thermodynamic limit), however, one obtains the so-called Bethe approximation. Here we study such a local description by setting up a simple recurrence relation for successive shell magnetizations far removed from the surface. In the ferromagnetic case the local magnetization is a fixed point of the iterative transformation, while in the antiferromagnetic case the fixed point bifurcates to a two-cycle of the transformation (for low temperatures and fields) giving rise to local sublattice magnetizations. In both cases, local thermodynamical properties are obtained by integration.
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    Metastability and the Ising model (1982)
    Springer
    Journal of statistical physics 27 (1982), S. 657-675 
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    ISSN: 1572-9613
    Keywords: Metastability ; Ising model ; Glauber dynamics
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    Notes: Abstract We discuss a recent theorem which establishes a precise connection between (i) the approximate degeneracy of the zero eigenvalue for the generator of the Glauber dynamics of the Ising model in a small nonzero field and below the critical temperature, (ii) the existence of a partition of the configuration space into a normal region and a metastable region. This enables us to demonstrate that the recent approach to metastability of Davies and Martin may be viewed as a simple (although in some ways fairly crude) approximation to the conventional approach. We also obtain what appear to be the first results concerning the stability of metastable states under small perturbations.
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    Correlation inequalities for the truncated two-point function of an Ising ferromagnet (1982)
    Springer
    Journal of statistical physics 29 (1982), S. 177-183 
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    ISSN: 1572-9613
    Keywords: Correlation inequalities ; Ising model
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    Topics: Physics
    Notes: Abstract We establish the following new correlation inequalities for the truncated twopoint function of an Ising ferromagnet in a positive external field: 〈σ j ; σ l 〉 T ⩾〈σ j ; σ k 〉 T 〈σ k ;σ l 〉 T , and 〈σ j ; σ l 〉 T ⩽ ∑ k ∈ K 〈σ j ; σ k 〉 T 〈σ k σ l 〉, whereK is any set of sites which separatesj froml. The inequalities are also valid for the pure phases with zero magnetic field at all temperatures. Above the critical temperature they reduce to known inequalities of Griffiths and Simon, respectively.
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    An improvement of the Griffiths-Hurst-Sherman inequality for the Ising ferromagnet (1982)
    Springer
    Journal of statistical physics 29 (1982), S. 185-191 
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    ISSN: 1572-9613
    Keywords: Correlation inequalities ; Ising model
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    Topics: Physics
    Notes: Abstract We prove the following inequality for the truncated correlation in the Ising model in zero external field: $$\begin{gathered} \langle \sigma _i \sigma _j \sigma _k \sigma _l \rangle - \langle \sigma _i \sigma _j \rangle \langle \sigma _k \sigma _l \rangle - \langle \sigma _i \sigma _k \rangle \langle \sigma _j \sigma _l \rangle - \langle \sigma _i \sigma _l \rangle \langle \sigma _j \sigma _k \rangle \hfill \\ \leqslant - 2\langle \sigma _i \sigma _m \rangle \langle \sigma _j \sigma _m \rangle \langle \sigma _k \sigma _m \rangle \langle \sigma _l \sigma _m \rangle \hfill \\ - 2 \left( {\langle \sigma _i \sigma _k \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right) \left( {\langle \sigma _j \sigma _k \rangle - \langle \sigma _j \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right)\langle \sigma _k \sigma _l \rangle \hfill \\ - 2 \langle \sigma _i \sigma _m \rangle \langle \sigma _j \sigma _m \rangle \left( {\langle \sigma _i \sigma _k \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _k \rangle } \right)\left( {\langle \sigma _i \sigma _l \rangle - \langle \sigma _i \sigma _m \rangle \langle \sigma _m \sigma _l \rangle } \right) \hfill \\ \end{gathered} $$ This inequality is a strengthening of the Lebowitz inequality for the four-point function and implies the following improvement of the GHS inequality: $$\langle \sigma _i ;\sigma ;_j \sigma _k \rangle ^T \leqslant - 2\langle \sigma _i ;\sigma _k \rangle ^T \langle \sigma _j ;\sigma _k \rangle ^T \langle \sigma _k \rangle $$ This in turn implies the critical exponent inequality $$\Delta '_3 \geqslant \gamma ' - \beta $$
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    Analytic continuation at first-order phase transitions (1982)
    Springer
    Journal of statistical physics 29 (1982), S. 205-229 
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    ISSN: 1572-9613
    Keywords: First-order phase transitions ; analytic continuation ; metastable states ; Ising model ; essential singularity ; spinodal
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    Topics: Physics
    Notes: Abstract We study the analytic structure of thermodynamic functions at first-order phase transitions in systems with short-range interactions and in particular in the two-dimensional Ising model. We analyze the nature of the approximation of the d=2 system by anN × ∞ strip. Investigation of the structure of the eigenvalues of the transfer matrix in the vicinity of H=0 in the complexH plane allows us to define a new function which provides rapidly convergent approximations to the stable free energyf and its derivatives for allH ⩾ 0. This new function is used for numerical calculation of the coefficients Cn in the power series expansions of the magnetizationm in the form m(H)=1 + ∑Cn(H-H 0 )n for various H0⩾ 0. The resulting series are studied by conventional methods. We confirm recent series analysis results on the existence of the droplet model type essential singularity at H=0. Evidence is found for a spinodal at H=Hsp(Ti 〈 0.
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    On the ferromagnetic Ising model in noninteger spatial dimension (1982)
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    Journal of statistical physics 29 (1982), S. 699-716 
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    ISSN: 1572-9613
    Keywords: Ising model ; Yang-Lee theorem ; dimensional analytic continuation ; series expansions methods
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    Notes: Abstract Using the necessary and sufficient conditions in terms of the high-field series coefficients that the Yang-Lee theorem holds, we prove rigorously by counterexample that it cannot be extended to general noninteger dimension, when such models are defined by the “natural” analytic continuation.
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    Phase separations in Ising model with free boundary condition (1983)
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    Journal of statistical physics 30 (1983), S. 1-13 
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    ISSN: 1572-9613
    Keywords: Ising model ; Gibbs measure ; phase separation ; phase transition ; contour ; conditional Gibbs measure
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    Notes: Abstract We consider the problem of phase separations in Ising model with free boundary condition. We prove that-a typical configuration has just one open contour λ which separatesV into two parts which are occupied by the opposite phases. λ is the shortest possible contour compatible with the condition thatV is divided by λ into two regions of area p¦V¦ and (1-p)V¦.
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    Solvable models in statistical mechanics, from Onsager onward (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 7-16 
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    ISSN: 1572-9613
    Keywords: Statistical mechanics ; lattice models ; Ising model ; solvable models ; integrable systems ; Yang-Baxter relations
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    Topics: Physics
    Notes: Abstract There is now a whole field in mathematical physics concerned with solvable models in statistical mechanics, field theory, and related areas. We indicate the influence that Onsager's solution of the planar Ising model has had, and continues to have, on this field.
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    Ising metamagnet under staggered field (1995)
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    Journal of statistical physics 81 (1995), S. 837-842 
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    ISSN: 1572-9613
    Keywords: Ising model ; staggered field ; metastable state
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    Notes: Abstract We report a Monte Carlo simulation of the layered Ising antiferromagnet under an external magnetic field. We show that under a staggered field, there occurs a phase transition from a metastable state which follows a Vogel-Fulcher law. For a staggered intrasublattice interaction a similar situation occurs.
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    Constrained variational problem with applications to the Ising model (1996)
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    Journal of statistical physics 83 (1996), S. 867-905 
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    ISSN: 1572-9613
    Keywords: Ising model ; Wulff shape ; large deviations ; boundary effects
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    Notes: Abstract We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic fieldh, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (−)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of orderB/h withB small enough, while ifB is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical valueB 0 (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a “squeezed Wulff shape”. The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.
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    One-dimensional random-field ising model: Gibbs states and structure of ground states (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 1077-1093 
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    ISSN: 1572-9613
    Keywords: Gibbs states ; ground states ; residual entropy ; random field ; Ising model
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    Notes: Abstract We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibb state is unique for any realization of the external field. Then we prove that asT→0, the Gibbs state converges to a limit, a ground state, for almost all realizations of the external field. The ground state turns out to be a probability measure concentrated on an infinite set of configurations, and we give a constructive description of this measure.
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    Phase transitions in phosphatidylcholine foam bilayers (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 147-160 
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    ISSN: 1572-9613
    Keywords: Foam bilayer ; phase transition ; Ising model ; mean-field ; binding energy
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    Notes: Abstract Foam bilayers from individual and mixed phosphatidylcholines are experimentally studied at different temperatures. Occurrence of a chain-melting phase transition in the foam bilayers is detected by two independent parameters—the critical concentrationC c for formation of foam bilayer and the foam bilayer thickness. The data forC c are discussed on the basis of the hole-nucleation theory, which applies the Ising model to foam bilayers and uses the mean-field approximation for interpretation of their stability. This allows the determination of the binding energy of a phospholipid molecule in gel and liquid-crystalline foam bilayers. New possibilities to relate the microscopic and macroscopic characteristics of foam bilayers are demonstrated.
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    Stacking order and disorder in layered K3Me(CN)6 compounds studied by diffuse X-ray scattering: A realization of the ANNNI model? (1995)
    Springer
    Journal of statistical physics 78 (1995), S. 135-145 
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    ISSN: 1572-9613
    Keywords: Polytypism ; Ising model ; Order-disorder ; X-ray scattering
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    Notes: Abstract Layered crystalline materials like K3Me(CN)6 with Me=Cr, Mn, Fe, Co may often exist in various polytypic forms, due to a variety of choices of layer stacking modes. For cases where the interlayer constellations can be limited to only two energetically almost equivalent ways, the buildup of the crystal may be described by a spin-1/2 Ising-like model. For the system presently being studied one can rationalize the layer stacking to a four-valued choice (i.e., a 1D 4-state Potts case), or use an Ising-like two-sublattice model. Previous diffraction studies of K3Me(CN)6 indicated that two long-range ordered structures prevailed, an orthohombic one named MDO1, with one double layer per repetition unit, and a monoclinic one, MDO2, with two double-layer units. Our studies reveal a more complex situation: The Fe material is for the most part of the MDO2 type. But in addition, in some crystal samples, a hitherto unobserved phase also appears, with six double-layer repetition units, in fact a hybrid of MDO1 and MDO2. The Co material is for the most part of the MDO2 type, but contains in addition a considerable contribution of stacking disorder, as evidenced by the presence of diffuse X-ray scattering lines. The lines do, however, contain distinct maxima, indicating the presence of several layer stacking modes with preference of two, three, four, five, and seven double-layer correlations. The findings can be qualitatively discussed in terms of the ANNNI model.
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    A discrete variational problem related to Ising droplets at low temperatures (1995)
    Springer
    Journal of statistical physics 80 (1995), S. 103-123 
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    ISSN: 1572-9613
    Keywords: Discrete variational problem ; Ising model ; droplets ; metastability
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    Notes: Abstract We consider a variational problem on thed-dimensional latticeZ d which has applications in the study of the meatastable behavior of the stochastic Ising model. The problem, an isoperimetric one, is to find what is the smallest area a finite subset ofZ d can have restricted to three classes of subsets ofZ d . If ϕ is one of these subsets, we define its volume as the number of points in it and its area as the number of pairs of points inZ d which are neighbors and such that only one of them belongs to ϕ.
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    Renormalization group at criticality and complete analyticity of constrained models: A numerical study (1997)
    Springer
    Journal of statistical physics 86 (1997), S. 1117-1151 
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    Keywords: Majority rule ; renormalization group ; non-Gibbsianness ; finite-size conditions ; complete analyticity ; Ising model
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    Notes: Abstract We study the majority rule transformation applied to the Gibbs measure for the 2D Ising model at the critical point. The aim is to show that the renormalized Hamiltonian is well defined in the sense that the renormalized measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman uniqueness (DSU) finite-size condition for the “constrained models” corresponding to different configurations of the “image” system. It is known that DSU implies, in our 2D case, complete analyticity from which, as recently shown by Haller and Kennedy. Gibbsianness follows. We introduce a Monte Carlo algorithm to compute an upper bound to Vasserstein distance (appearing in DSU) between finite-volume Gibbs measures with different boundary conditions. We get strong numerical evidence that indeed the DSU condition is verified for a large enough volumeV for all constrained models.
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    On Criticality for Competing Influences of Boundary and External Field in the Ising Model (1998)
    Springer
    Journal of statistical physics 92 (1998), S. 35-45 
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    ISSN: 1572-9613
    Keywords: Competing influences ; Ising model ; Gibbs measures
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    Notes: Abstract We continue a study of Schonmann (1994), Schonmann and Shlosman (1996), and Greenwood and Sun (1997) regarding the competing influences of boundary conditions and external field for the Ising model. We find a critical point B 0 in the competing influences for low temperature in dimension d 2A7E; 2.
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    Critical Exponents of the Diluted Ising Model between Dimensions 2 and 4 (1998)
    Springer
    Journal of statistical physics 92 (1998), S. 785-808 
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    Keywords: Critical phenomena ; diluted spin systems ; Ising model ; renormalization group
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    Notes: Abstract Within the massive field-theoretic renormalization-group approach the expressions for the β and γ functions of the anisotropic mn-vector model are obtained for general space dimension d in three-loop approximation. Resumming corresponding asymptotic series, critical exponents for the case of the weakly diluted quenched Ising model (m = 1, n = 0), as well as estimates for the marginal order parameter component number m c of the weakly diluted quenched m-vector model, are calculated as functions of d in the region 2 ≤ d 〈 4. Conclusions concerning the effectiveness of different resummation techniques are drawn.
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    Ising-Model, Block-Spin Distributions by the Markov Property Method (1998)
    Springer
    Journal of statistical physics 93 (1998), S. 573-582 
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    ISSN: 1572-9613
    Keywords: Scaling ; Ising model ; Markov property ; critical phenomena ; parallel computational procedures
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    Notes: Abstract The idea that near the critical point each block of spins behaves just like a single big spin is investigated. The case where a diamond-shaped block of spins is embedded in a (small) sea of spins is studied. Use is made of the Markov property method to make exact computations of the various spin moments needed to test this hypothesis. The residual fluctuation about the mean value of the block spin is seen to tend to a finite fraction of the length of the mean block-spin. This result is in line with previous studies which used different types of boundary conditions.
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    On the Ising Model with Strongly Anisotropic External Field (1999)
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    Journal of statistical physics 97 (1999), S. 87-144 
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    ISSN: 1572-9613
    Keywords: Ising model ; anisotropic field ; phase diagram ; cluster expansion
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    Notes: Abstract In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.
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    Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus (2000)
    Springer
    Journal of statistical physics 98 (2000), S. 551-588 
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    ISSN: 1572-9613
    Keywords: Ising model ; universal amplitude ratios ; conformal field theory ; torus ; finite-size scaling ; corrections to scaling ; Monte Carlo ; Swendsen–Wang algorithm ; cluster algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x ★=lim L→∞ ξ(L)/L and the first four magnetization moment ratios V 2n =〈 $$M$$ 2n 〉/〈 $$M$$ 2〉 n . As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G*2n . We confirm these predictions by a high-precision Monte Carlo simulation.
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    URL: http://dx.doi.org/10.1023/A:1018611122166
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    Distribution of Energies for the Two-Dimensional Ising Model (2000)
    Springer
    Journal of statistical physics 98 (2000), S. 1063-1073 
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    ISSN: 1572-9613
    Keywords: polygon statistics ; Ising model ; exact solution
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    Topics: Physics
    Notes: Abstract We calculate the number of polygons with fixed total length drawn on a square lattice with periodic boundary conditions. In addition, we study the statistics of polygons with the number of horizontal and vertical links fixed separately. The analysis is performed via a mapping to the Ising model with isotropic and anisotropic interactions. We deal with the case of finite lattice sizes as well as the thermodynamic limit.
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    URL: http://dx.doi.org/10.1023/A:1018659510760
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    Thermal Conductivity of 2223 BSCCO Superconductor–Polyethylene Glycol Composites Between 20 and 300 K (2000)
    Springer
    Journal of superconductivity 13 (2000), S. 417-422 
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    ISSN: 1572-9605
    Keywords: (Bi,Pb)2223-PEG composites ; thermal conductivity ; polyethylene glycol
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract Thermal conductivity measurements have been taken between 20 and 300 K on composites prepared from polyethylene glycol (PEG) containing various amounts of superconducting (Bi,Pb)2223 powder. The nature of temperature variation of thermal conductivity (λC) of the composites and its magnitude depend strongly on the volume concentration of the high-temperature superconductor (HTSC) filler present in the material. The results have been discussed in the light of models known for polymer–metal powder composites. It is shown that for composites with 2223 powder content 〈44 vol. %, the measured data can be accounted well with Hamilton–Crosser model, taking the sphericity factor into consideration. Failure of Hamilton–Crosser expression for composites with higher filler concentration is thought to be associated with direct contact between the superconducting grains, which shortcircuits the acoustic mismatch resistance in the composites.
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    URL: http://dx.doi.org/10.1023/A:1007755125840
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    Dynamic Monte Carlo renormalization group (1983)
    Springer
    Journal of statistical physics 33 (1983), S. 1-11 
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    ISSN: 1572-9613
    Keywords: Renormalization group ; Monte Carlo ; dynamic critical phenomena ; Glauber and Kawasaki models ; Ising model ; finite-size scaling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new and simple method of applying the idea of real space renormalization group theory to the analysis of Monte Carlo configurations is proposed and applied to the Glauber kinetic Ising model in two and three dimensions, and to the Kawasaki model in two dimensions. Our method, if correct, utilizes how the system approaches its equilibrium; in contrast to most other Monte Carlo investigations there is no need to wait until equilibrium is established. The renormalization analysis takes only a small fraction of the computer time needed to produce the Monte Carlo configurations, and the results are obtained as the system relaxes atT =T c , the critical temperature. The values obtained for the dynamical critical exponent,z, are 2.12 (d=2) and 2.11 (d=3) for the Glauber model, the 3.90 for the two-dimensional Kawasaki model. These results are in good agreement with those obtained by other methods but with smaller error bars in three dimensions.
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    Magnetization concavity in ferromagnets (1983)
    Springer
    Journal of statistical physics 33 (1983), S. 91-98 
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    ISSN: 1572-9613
    Keywords: Ising model ; magnetization ; concavity ; correlation inequality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We investigate the conjecture that in Ising ferromagnets, single-site magnetization 〈σ n 〉 is a jointly concave function of the magnetic field variables. We present partial results favoring the conjecture, including a numerical survey, although we do not prove it in full generality. We also point out some implications of concavity.
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    On the nature of the nearest singularities of the free energy in the neighborhood of a critical point (1983)
    Springer
    Journal of statistical physics 33 (1983), S. 43-58 
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    ISSN: 1572-9613
    Keywords: Algebraic function ; branch points ; critical point ; free energy ; Ising model ; Riemann surface ; singularity ; spinodal line
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Algebraic functions are used to provide an example of multiple-valued functions which coincide with a model (single-valued) free energy on one sheet of the Riemann surface in the neighborhood of a critical point. For the case of homogeneous free energies andα=α′=0, there are enough conditions to determine the behavior of the nearest singularities (branch points) to the critical point of the algebraic function. If no other singularities are present these branch points would represent the spinodal line. The particular exponents of the two-dimensional Ising model are used to provide a specific example.
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    Analyticity properties and a convergent expansion for the inverse correlation length of the high-temperatured-dimensional Ising model (1984)
    Springer
    Journal of statistical physics 34 (1984), S. 597-608 
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    ISSN: 1572-9613
    Keywords: Ising model ; correlation length ; correlation function ; expansion for correlation length ; analyticity of correlation length ; high-temperature Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We show that the inverse correlation lengthm(β) (= mass of the fundamental particle of the associated lattice quantum field theory) of the spin-spin correlation function 〈s x s y 〉,x, y εZ d , of thed-dimensional Ising model admits the representation $$m(\beta ) = - ln\beta + r(\beta )$$ for small inverse temperaturesβ 〉 0.r(β) is ad-dependent function, analytic atβ = 0.c n , the nth β = 0 Taylor series coefficient of r(β) can be computed explicitly from the Zd limit of a finite number of finite lattice A spin-spin correlation functions 〈s0sx〉t〉Afor a finite number ofx = (x 1,x2, ..., xd), ¦x¦ = ∑ i d 1¦xi¦〈 R(n), where R(n) increases withn. Furthermore, there exists aβ' 〉 0, such that for eachβ ε (0,β')m(β) is analytic. Similar results are also obtained for the dispersion curve ω(p), ω(p)=ω(0)=m, pε(-π, π]d−1, of the fundamental particle of the associated lattice quantum field theory.
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    Analyticity properties and a convergent expansion for the inverse correlation length of the low-temperatured-dimensional Ising model (1984)
    Springer
    Journal of statistical physics 34 (1984), S. 609-614 
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    ISSN: 1572-9613
    Keywords: Ising model ; correlation length ; correlation length expansion ; low-temperature Ising model ; correlation function
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    Topics: Physics
    Notes: Abstract We show that the inverse correlation lengthm(z) of the truncated spin-spin correlation function of theZ d Ising model with + or — boundary conditions admits the representationm(z) = −(4d−4)ln z(1−δd1) + r(z) for smallz=e −β, i.e., large inverse temperatures $$\beta 〉 0.r(z) = \Sigma _{n = 1}^\infty b_{n^{Z^n } } $$ is ad-dependent analytic function atz = 0, already known in closed form ford = 1 and 2; ford = 3 bn can be computed explicitly from a finite number of the Zd limits of z = 0 Taylor series coefficients of the finite lattice correlation function at a finite number of points ofZ d.
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    Behavior of the effective fields for a regular ising model on the Cayley tree (1984)
    Springer
    Journal of statistical physics 35 (1984), S. 355-374 
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    ISSN: 1572-9613
    Keywords: Ising model ; Cayley tree ; frustration ; mapping ; fixed points ; period ; arithmetic furcation ; screening of furcations ; spin glass ; spin crystal
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A regular Ising model with nearest-neighbor interactions ofJ and−J(J〉0) on a Cayley tree of coordination number 3 is investigated for the behavior of effective fields in a uniform external field. The effective fields show periodic and also aperiodic structures in the temperature-field plane. At absolute zero temperature, the equations determining effective fields are reduced to a nonlinear, one-dimensional, iterative equation. Arithmetic furcations of period and a “screening” of the furcations are observed.
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    A geometric interpretation of the roughening transition in Ising models (1984)
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    Journal of statistical physics 35 (1984), S. 473-488 
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    ISSN: 1572-9613
    Keywords: Roughening transition ; Ising model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Progress in the area of the Ising model roughening transition has previously been limited by the lack of a good definition for the interface separating the pure phases. In the present work, a graphical definition is introduced and it is shown that roughening occurs precisely when this interface fluctuates to infinity.
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    Monte Carlo simulation of Ising models by multispin coding on a vector computer (1984)
    Springer
    Journal of statistical physics 37 (1984), S. 271-282 
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    ISSN: 1572-9613
    Keywords: Ising model ; Monte Carlo method ; multispin coding ; vector computer
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    Topics: Physics
    Notes: Abstract Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.
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    URL: http://dx.doi.org/10.1007/BF01011834
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    A new multispin coding algorithm for Monte Carlo simulation of the Ising model (1984)
    Springer
    Journal of statistical physics 37 (1984), S. 283-299 
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    ISSN: 1572-9613
    Keywords: Ising model ; Monte Carlo ; multispin coding ; parallel computation
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    Topics: Physics
    Notes: Abstract We present a new algorithm for Monte Carlo simulation of the Ising model. The usual serial architecture of a computer is exploited in a novel way, enabling parallel but independent calculations to be carried out on as many spins as there are bits in a computer word in each fundamental move. The algorithm enjoys a substantial increase in execution speed over more usual multispin coding algorithms. By its very nature, the algorithm constitutes a design for a special-purpose processor.
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    Phase transitions in the Ising model with transverse field (1984)
    Springer
    Journal of statistical physics 37 (1984), S. 407-417 
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    ISSN: 1572-9613
    Keywords: Ising model ; phase transition ; reflection positivity
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    Notes: Abstract We show the existence of a phase transition in the Ising model with transverse field for dimensionsv ≥ 2 provided the transverse term is sufficiently small. This is done by proving long-range order occurs using the reflection positivity of the Hamiltonian and localization of eigenvectors.
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    The rate of falloff of Ising model correlations at large temperature (1981)
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    Journal of statistical physics 26 (1981), S. 53-58 
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    ISSN: 1572-9613
    Keywords: Ising model ; high temperature ; correlation delay
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    Notes: Abstract We recover results of Abraham and Kunz and Paes-Leme on falloff of Ising model correlations at high temperature by using nothing more than high-temperature diagrams.
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    Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model (1995)
    Springer
    Journal of statistical physics 80 (1995), S. 1309-1326 
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    ISSN: 1572-9613
    Keywords: Renormalization group ; position-space renormalization-group transformations ; Ising model ; low-temperature expansions
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.
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    Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model (1996)
    Springer
    Journal of statistical physics 84 (1996), S. 85-118 
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    ISSN: 1572-9613
    Keywords: Ising model ; Markov chain ; transfer matrix ; Friedrichs model ; saddle-point method ; scattering theory ; T-matrix
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    Topics: Physics
    Notes: Abstract We find the asymptotic decrease of correlations 〈σ A +y ,σ B 〉,y∈Z v +1, |y|→∞, in the Ising model at high temperatures. For the case when monomialsσ A andσ B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension ν. For even monomialsσ A ,σ B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) ν=1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary ν. Here we use besides the saddle-point method, some arguments from scattering theory.
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    Ising models on the lattice Sierpinski gasket (1996)
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    Journal of statistical physics 84 (1996), S. 295-307 
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    Keywords: Ising model ; lattice Sierpinski gasket ; Dobrushin-Shlosmann mixing condition
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    Topics: Physics
    Notes: Abstract Ferromagnetic Ising models on the lattice Sierpinski gasket are considered. We prove the Dobrushin-Shlosmann mixing condition and discuss corresponding properties of the stochastic Ising models.
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    The roughening transition of the three-dimensional Ising interface: A Monte Carlo study (1996)
    Springer
    Journal of statistical physics 85 (1996), S. 383-401 
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    ISSN: 1572-9613
    Keywords: Ising model ; roughening transition ; Monte Carlo ; finite-size scaling ; renormalization group
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    Notes: Abstract We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite-size scaling method. The particular method has recently been proposed and successfully tested for various solid-on-solid models. The basic idea is the matching of the renormalization-groupflow of the interface with that of the exactly solvable body-centered cubic solid-on-solid model. We unambiguously confirm the Kosterlitz-Thouless nature of the roughening transition of the Ising interface. Our result for the inverse transition temperatureK r=0.40754(5) is almost two orders of magnitude more accurate than the estimate of Mon, Landau, and Stauffer.
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    Status of the round robin on the transport properties of R134a (1995)
    Springer
    International journal of thermophysics 16 (1995), S. 63-78 
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    ISSN: 1572-9567
    Keywords: R134a ; dilute gas ; refrigerant ; saturation properties ; 1,1,1,2-tetrafluoroethane ; thermal conductivity ; transport properties ; viscosity
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    Notes: Abstract The paper contains a status report on an international project coordinated by the Subcommittee on Transport Properties of Commission 1.2 of the International Union of Pure and Applied Chemistry. The project has been conducted to investigate the large discrepancies between the results reported by various authors for the transport properties of R134a. The project has involved the remeasurement of the transport properties of a single sample of R134a in nine laboratories throughout the world in order to test the hypothesis that at least part of the discrepancy could be attributed to the purity of the sample. This paper provides an intercomparison of the new experimental results obtained to data in this project for the viscosity and the thermal conductivity in both gaseous and liquid phases. The agreement between the viscosity data from the laboratories contributing to the project was improved with several techniques, now producing consistent results. This suggests that the purity of the samples of R134a used in previous work was at least partly reponsible for the discrepancies observed. For the thermal conductivity in the liquid phase the results of the measurements are also more consistent than before, although not for all experimental techniques. Not all of the previous measurements suffered from significant sample impurities, so the present measurements on a consistent high-purity sample can he used to detect data sets which are outhers, possibly because of impurities. Identification of laboratories and techniques with systematic differences may require the examination of data for several fluids. The implications for future measurements of the transport properties of other refrigerants are significant.
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    Temperature oscillation techniques for simultaneous measurement of thermal diffusivity and conductivity (1995)
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    International journal of thermophysics 16 (1995), S. 413-422 
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    ISSN: 1572-9567
    Keywords: ethanol ; heptane ; nonane ; periodic techniques ; temperature ocillations ; thermal conductivity ; thermal dill'usivity ; water
    Source: Springer Online Journal Archives 1860-2000
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    Notes: Abstract Simple temperature ocillation techniques are described for the last measurement of thermal dill'usivity and conductivity of liquids. The liquid specimen is a slab bounded above and below by a reference material. Two Peltier elements mounted on the outer Surfaces of the reference layers generate temperature ocillationS of these surfaces. Temperature waves propagate tluough the reference layers into the specimen. The thermal dilhusivity of the specimen is deduced by measuring all evaluating the amplitude attenuation and or the phase shift between the fundamental temperature oscillations at the surface of the liquid specimen and at a well-defined position inside the specimen. If the thermal diffusivity of the specimen is known. the thermal conductivity is determined by the measured amplitude attenuation and or the phase shill between the fundamental temperature oscillations at the surface of the reference layer and at the surface of the specimen. Slab and semi-infinite body geometries are considered. Measurement cells are designed and experiments are carried out with water, ethanol. heptane. monane. and glycerine. The results of the measurements of thermal dilhusivity asree very well, and those of thermal conductivity reasonably well, with the data obtained from the literature.
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    Measurements of the Thermal Conductivity of HFC-125 in the Temperature Range from 300 to 515 K at Pressures up to 53 Mpa (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 375-399 
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    ISSN: 1572-9567
    Keywords: coaxial cylinders ; high pressure ; refrigerants ; HFC-125 ; thermal conductivity
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    Notes: Abstract Measurements of the thermal conductivity of HFC-125 that have been made by a coaxial cylinder cell operating in steady state are reported. The measurements of the thermal conductivity of HFC-125 were performed along several quasi-isotherms between 300 and 515 K in the gas phase and the liquid phase. The pressure range covered varies from 0.1 to 53 MPa. Based on the measurement of more than 600 points, an empirical equation is provided to describe the thermal conductivity outside the critical region as a function of temperature and density. A careful analysis of the various sources of error leads to an estimated uncertainty of approximately ± 1.5%.
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    Thermophysical Properties of Swine Myocardium (1999)
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    International journal of thermophysics 20 (1999), S. 665-676 
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    ISSN: 1572-9567
    Keywords: density ; myocardium ; swine ; thermal conductivity ; thermal diffusivity
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    Notes: Abstract This paper presents the experimental technique and results for the thermal conductivity, thermal diffusivity, and density of swine myocardial tissue. These properties were measured for freshly excised tissue. Thermal properties were measured using a self-heated thermistor probe, while the density was measured using a water displacement method. Thermistor probes were inserted into the tissue of interest and were used to supply heat within the tissue as well as to monitor the temperature rise in the tissue. An empirical calibration procedure was used to measure the properties of the tissue at different temperatures. The measurement instrument was first calibrated against agar-gelled water and glycerol at each temperature. The measurements were made at temperatures of 25, 37, 50, 62, and 76°C. The uncertainty in the measurement ranges from 2% at lower temperatures to about 5% at higher temperatures (T 〉 50°C). The properties of the tissue depend significantly on the water content. At temperatures higher than 50°C, there is significant water loss from the tissue during the procedure. The water loss is found to vary exponentially with the increase in temperature relative to ambient. Consequently, there is a decrease in the thermal conductivity values with increasing temperature. This decrease, however, is not as much as one would expect from the water loss data. A hypothesis to explain the relationships among water loss, cell damage, and thermal properties is proposed.
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    The thermal conductivity of binary mixtures of liquid R22 with R142b and R152a at low temperatures (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 597-606 
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    ISSN: 1572-9567
    Keywords: binary mixtures ; low temperatures refrigerants ; R22 ; R1426 ; R152a ; thermal conductivity ; transient method
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    Notes: Abstract The paper presents the thermal conductivity of mixtures of liquid refrigerants, The group of systems studied consists of two binary mixtures of R22/R142b and R22/R152a. The measurements have been carried out in the temperature range 160–300 K for pressures From 0.2 to 8.0 MPa in a transient coaxial-cylinder instrument. The uncertainty of the thermal conductivity data is estimated to be ±2%. The experimental method and apparatus were validated by using the measurements of refrigerant R22. The results presented have been used to develop a correlation for the description of the thermal conductivity of refrigerants.
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    Thermal conductivity of alternative refrigerants in the liquid phase (1996)
    Springer
    International journal of thermophysics 17 (1996), S. 561-571 
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    Keywords: alternative refrigerants ; difluoromethane (HFC-32) ; pentafluoroethane (HFC-125) ; 1,1,1-trifluoroethane (HFC-143a) ; dichloropentafluoropropanes (HCFC-225ca, HCFC-225cb) ; liquid phase ; thermal conductivity
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    Notes: Abstract Measurements ofthe thermal conductivity of five alternative refrigerants. namely, difluoromethane HFC-321. pentafluoroethane (HFC-125), 1,1,1-trifluoroethane (HFC-143a), and dichloropentafluoropropanes (HCFC-225ca and HCFC-225cb). are carried out in the liquid phase, The range of temperature is 253–324 K for HFC-32, 257–305 K for HFC-125, 268–314 K for HFC-134a. 267–325 K for HCFC-225ca, and 286–345 K for HCFC-225cb, The pressure rank is from saturation to 30 MPa, The reproducibility of the data is better than 0.5% and the accuracy of the data is estimated to be of the order of 1%. The experimental results for the thermal conductivity ofeach substance are correlated by an equation which is a function of temperature and pressure. A short discussion is given to the comparison of the present results with literature values for HFC-125, The saturated liquid thermal conductivity values of HFC-32. HFC-125, and HFC-143a are compared with those of chlorodifluoromethane (HCFC-22) and tetrafluoroethane (HFC-134a) and it is shown that the value of HFC-32 is highest, while that of HFC-125 is lowest, among these substances, The dependence of thermal conductivity on number of fluorine atoms among the refrigerants with the same number of carbon and hydrogen atoms is discussed.
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    Thermal Conductivity and Thermal Diffusivity of Pulse-Heated W–Re Alloys (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1237-1246 
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    ISSN: 1572-9567
    Keywords: electrical resistivity ; enthalpy ; high temperature ; liquid alloys ; rhenium alloys ; specific heat ; thermal conductivity ; thermal diffusivity ; tungsten alloys
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Results are reported for the thermal conductivity and thermal diffusivity as a function of temperature for four W–Re alloys (4.0, 21.24, 24.07, and 31.09 mass% of Re) over a wide temperature range covering the solid and liquid states. The measurements allow the determination of specific heat and dependences among electrical resistivity, temperature, and density of the alloys into the liquid phase. The thermal conductivity is calculated using the Wiedeman–Franz law. Additionally, data for thermal conductivity and thermal diffusivity of the constituent elements, tungsten and rhenium, are presented for the first time. Both metals have been previously studied with the same experimental technique.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022627525523
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    Electronic Resource
    Electronic Resource
    Thermal Conductivity of Binary Refrigerant Mixtures of HFC-32/125 and HFC-32/134a in the Liquid Phase (1999)
    Springer
    International journal of thermophysics 20 (1999), S. 1403-1415 
    Details
    ISSN: 1572-9567
    Keywords: HFC-32/125 ; HFC-32/134a ; binary mixture ; refrigerant ; thermal conductivity ; transient hot-wire method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The liquid thermal conductivity of mixtures of HFC-32/125 and HFC-32/134a was measured using the transient hot-wire apparatus in the temperature ranges from 213 to 293 K and from 193 to 313 K, respectively, in the pressure range from 2 to 30 MPa and with HFC-32 mass fractions of 0.249, 0.500, and 0.750 for each system. The uncertainty of the thermal conductivity was estimated to be ±0.7%. For practical applications, the thermal conductivity data for the two mixtures were represented by a polynomial in temperature, pressure, and mass fraction of HFC-32 with a standard deviation of 1.0%.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021432920199
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