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  • Articles  (558)
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  • Articles  (558)
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  • 1
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    Springer
    Letters in mathematical physics 46 (1998), S. 207-218 
    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.
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  • 2
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    Marine geophysical researches 13 (1991), S. 311-329 
    ISSN: 1573-0581
    Keywords: thermal conductivity ; heat flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Physics
    Notes: Abstract Heat flow data provide constraints on the thermal structure and evolution of the oceanic lithosphere. Because precise determination of the heat flux requires that both the thermal gradient and the thermal conductivity be well determined we have examined the thermal conductivities used in a new Pacific Basin heat flow data set. ∼43% of the ∼1600 heat flow determinations rely on values estimated by various methods, rather than directly measured. Although the measured and estimated conductivities have comparable means, the measured conductivities have a standard deviation ∼50% larger than the estimated, suggesting that the estimated values underestimate the actual variation. We investigate the limitations of using such estimates by examining factors controlling the variations of measured conductivity values. We find that the variation between the closest adjacent sites increases with increasing separation, such that sites within 200 km are on average noticeably closer in conductivity than sites further apart. Contributing to this effect may be the variation of conductivity with lithology (with mean conductivity highest for carbonate oozes, intermediate for deep-sea clays, and least for siliceous oozes) and a possible trend of decreasing conductivity with increasing seafloor depth. Tests with the measured data suggest that the best method for estimating conductivity is using the mean value measured within 200 km. The mean of a larger geographical region is a somewhat poorer predictor, and using the oceanwide mean and the value at the nearest site are poorer still. Approximately 29% of the estimated values were not based on measurements from a reference site. For most others, the reference site was the nearest measurement from the same cruise, typically a large distance away. For those sites where conductivity was not measured, 78% had measured conductivity within 200 km and were reestimated using the local mean, whereas the remaining 22% were reestimated using the regional mean. The resulting change in the estimated conductivity averaged ∼9% using the local mean and ∼6% using the regional mean. We suggest that such a procedure be used to improve the utility of the heat flow data set, as an alternative to discarding the large fraction of the available data that does not incorporate measured conductivities.
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  • 3
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    Letters in mathematical physics 37 (1996), S. 137-143 
    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.
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  • 4
    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.
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  • 5
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    Journal of superconductivity 13 (2000), S. 617-621 
    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.
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  • 6
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    Journal of statistical physics 11 (1974), S. 363-377 
    ISSN: 1572-9613
    Keywords: Ising model ; alloy ; disorder ; Bethe-Peierls approximation
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    Topics: Physics
    Notes: Abstract We study the Ising model for an alloy with an arbitrary number of components. We develop an approximation which reduces to that of Bethe and Peierls when the concentration of one of the components is unity. We investigate within this approximation the dependence of the various thermodynamic quantities, in particularT c, on the composition of the alloy and the magnetic properties of its constituents. Comparison with the only exact calculation available, that of F. T. Leeet al., for a linear chain, shows extremely satisfactory agreement.
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  • 7
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    Journal of statistical physics 13 (1975), S. 283-300 
    ISSN: 1572-9613
    Keywords: Diffusion ; gases ; kinetic theory ; Sutherland-Wassiljewa relations ; thermal conductivity ; time correlation functions ; viscosity
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    Topics: Physics
    Notes: Abstract A method of successive approximations is proposed for the evaluation of the time-correlation functions such as those that give the thermal transport coefficients of gases. The method is based on a calculation of the changes in correlations of appropriate functions of the molecular velocity which are a result of collisions in the gas. The decaying rates of the correlations are expressed as integrals of the differential collision cross section. When the first approximation is introduced in the expressions for thermal transport coefficients, results are obtained for the coefficient of binary diffusion and the viscosity and thermal conductivity of single-component systems which are identical with those of the first Chapman-Enskog solutions of the Boltzmann and Enskog equations. For the coefficients of viscosity and thermal conductivity in multicomponent systems, it is shown that the first approximation leads to expressions of the form of the Sutherland and Wassiljewa relations, respectively.
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  • 8
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    Journal of statistical physics 16 (1977), S. 149-168 
    ISSN: 1572-9613
    Keywords: Stochastic dynamics ; Ising model ; thermal bath ; master equation ; Markov process ; nonequilibrium thermodynamics
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    Topics: Physics
    Notes: Abstract With the help of recent results in the mathematical theory of master equations, we present a rigorous derivation of the stochastic Glauber dynamics of Ising models from Hamiltonian quantum mechanics. A thermal bath is explicitly constructed and, as an illustration, the dynamics of the Ising-Weiss model is analyzed in the thermodynamic limit. We thus obtain an example of a nonequilibrium statistical mechanical system for which a link without mathematical gap can be established from microscopic quantum mechanics to a macroscopic irreversible thermodynamic process.
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  • 9
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    Journal of statistical physics 16 (1977), S. 299-309 
    ISSN: 1572-9613
    Keywords: Ising model ; lattice gas ; nonuniform ; one-dimensional ; external field ; Ursell distributions ; direct correlations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The external potential needed to produce an arbitrary equilibrium density profile for a one-dimensional lattice gas with nearest neighbor interactions is solved exactly. The resulting sequence of direct correlation functions is shown to be of short range, and in the ferromagnetic case the even members alternate in sign at zero spin. The even Ursell distributions in this case likewise alternate in sign.
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  • 10
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    Journal of statistical physics 16 (1977), S. 339-348 
    ISSN: 1572-9613
    Keywords: Site percolation ; effective-medium theory ; random resistor network ; electrical conductivity ; thermal conductivity ; Monte Carlo experiment ; disordered materials
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A site percolation approach to classical transport in disordered two-phase materials is presented. A Monte Carlo computer experiment gives the bulk conductivity of a 30 x 30 x 30 site simple cubic resistor network consisting of two kinds of unit resistor with different conductance. A modified effective-medium theory predicts very accurately the bulk conductivity of the network. This theory is found to agree well with available data for the thermal conductivity of real two-phase materials: glass particle-silicon rubber; glass fiber-plastics; air-saturated porous sandstone; and air-saturated fire brick.
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  • 11
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    Journal of statistical physics 19 (1978), S. 405-415 
    ISSN: 1572-9613
    Keywords: Helix-coil transition ; heteropolymers ; Ising model ; melting ; correlated sequences
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Equations are derived for the calculation of the ground-state melting curves for polynucleotide sequences with correlation between the nearest neighbors. The case of arbitrary correlated sequences is also considered. The effect of correlations in the sequence on the width and on the intrinsic fine structure of melting curves is discussed.
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  • 12
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    Journal of statistical physics 20 (1979), S. 95-114 
    ISSN: 1572-9613
    Keywords: Ising model ; variational approximation ; spinor representatives ; crossover phenomena ; scaling
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    Topics: Physics
    Notes: Abstract The variational method developed by Baxter is applied to the zero-field Ising model on the square lattice. The problem is simplified to that of solving a relatively small system of nonlinear equations. The estimates to the spontaneous magnetization and the critical temperature from the sequence of variational approximations are obtained. The results converge rapidly to the exact ones. They exhibit a crossover phenomenon and satisfy a scaling relation.
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  • 13
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    Journal of statistical physics 22 (1980), S. 91-96 
    ISSN: 1572-9613
    Keywords: Renormalization group ; variational principles ; convexity ; bounds on free energy and internal energy ; Ising model
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    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.
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  • 14
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    Journal of statistical physics 25 (1981), S. 679-694 
    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.
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  • 15
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    Journal of statistical physics 25 (1981), S. 369-396 
    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.
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  • 16
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    Journal of statistical physics 27 (1982), S. 711-719 
    ISSN: 1572-9613
    Keywords: Ising model ; critical subdominant singularities ; series analysis of critical indices ; Pade approximants and mellin transform
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    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.
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  • 17
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    Journal of statistical physics 40 (1985), S. 249-257 
    ISSN: 1572-9613
    Keywords: Critical temperature ; Ising model ; correlation inequalities
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    Topics: Physics
    Notes: Abstract Upper bounds are obtained for spin ±1 systems. In the case of only nearestneighbor interactions on, for example, the square lattice we obtainΒ cJ〉0.3592. The method's strength is seen when considering systems with longer-range interactions. For example, we obtainΒ cJ〉0.360 compared to the previous best bound ofΒ c J⩾ 0.345 for the one-dimensional lattice with 1/r 2 interactions. The method relies upon an identity between correlation functions and then the use of correlation inequalities to obtain the final bounds.
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  • 18
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    Journal of statistical physics 26 (1981), S. 783-794 
    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.
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  • 19
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    Journal of statistical physics 46 (1987), S. 777-787 
    ISSN: 1572-9613
    Keywords: Interfaces ; interfacial free energy ; Ising model ; real-space renormalization
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    Topics: Physics
    Notes: Abstract The interfacial free energy of a two-dimensional Ising model is calculated by using various renormalization group schemes. The results obtained are quantitatively consistent with known exact results. In addition, a general discussion of various drawbacks within different renormalization group approximations is given. The best result are obtained with the 4×4 finite cluster approximation, while the Migdal-Kadanoff approximation seems to be inherently unsuitable for calculation of interfacial properties.
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  • 20
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    Journal of statistical physics 47 (1987), S. 343-374 
    ISSN: 1572-9613
    Keywords: Phase transition ; Ising model ; ϕ4 ; intermediate phase ; critical exponents ; inequalities
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    Topics: Physics
    Notes: Abstract For a family of translation-invariant, ferromagnetic, one-component spin systems—which includes Ising and ϕ4 models—we prove that (i) the phase transition is sharp in the sense that at zero magnetic field the high- and low-temperature phases extend up to a common critical point, and (ii) the critical exponent β obeys the mean field bound β⩽1/2. The present derivation of these nonperturbative statements is not restricted to “regular” systems, and is based on a new differential inequality whose Ising model version isM⩽βhχ+M 3+ βM 2∂M/∂β. The significance of the inequality was recognized in a recent work on related problems for percolation models, while the inequality itself is related to previous results, by a number of authors, on ferromagnetic and percolation models.
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  • 21
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    Journal of statistical physics 47 (1987), S. 931-938 
    ISSN: 1572-9613
    Keywords: Ising model ; random field ; diagrammatic expansion ; lower critical dimension ; metastability ; quasicriticality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Within the perturbation diagrammatic expansion we discuss the origin of differences in determinations of the lower critical dimension of the random-field Ising model and show that below four dimensions metastability and hysteresis occur. We also explain the occurrence of a quasicritical d=2 behavior at weak random fields, which is responsible for local stability of the ordered state above two dimensions.
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  • 22
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    Journal of statistical physics 78 (1995), S. 285-297 
    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.
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  • 23
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    Journal of statistical physics 78 (1995), S. 731-757 
    ISSN: 1572-9613
    Keywords: Ising model ; renormalization group ; finite-size conditions ; critical point
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    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.
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  • 24
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    Journal of statistical physics 78 (1995), S. 1311-1324 
    ISSN: 1572-9613
    Keywords: Random-cluster model ; Ising model ; Potts model ; comparison inequality ; BK inequality ; FKG inequality
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    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.
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  • 25
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    Journal of statistical physics 78 (1995), S. 1131-1138 
    ISSN: 1572-9613
    Keywords: Kac potential ; Ising model ; critical fluctuations ; Euclidean field theory
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    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.
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  • 26
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    Journal of statistical physics 74 (1994), S. 903-908 
    ISSN: 1572-9613
    Keywords: Dynamic critical exponent ; Ising model ; damage spreading
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    Notes: Abstract We measure the dynamic exponent of the three-dimensional Ising model using a “damage spreading” Monte Carlo approach as described by MacIsaac and Jan. We simulate systems fromL=5 toL=60 at the critical temperature,T c =4.5115. We report a dynamic exponent,z=2.35±0.05, a value much larger than the “consensus” value of 2.02, whereas if we assume logarithmic corrections, we find thatz=2.05±0.05.
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  • 27
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    Journal of statistical physics 82 (1996), S. 1299-1326 
    ISSN: 1572-9613
    Keywords: Cluster algorithms ; computational complexity ; diffusion-limited aggregation ; Ising model ; Metropolis algorithm ; P-completeness
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    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.
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  • 28
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    Journal of statistical physics 82 (1996), S. 1453-1466 
    ISSN: 1572-9613
    Keywords: Kinetic theory ; thermal conductivity ; molecular dynamics ; hard disks ; Enskog's Theory
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    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.
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  • 29
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    Journal of statistical physics 75 (1994), S. 67-121 
    ISSN: 1572-9613
    Keywords: Potts model ; Ising model ; random-cluster process ; critical temperature ; critical exponent ; differential inequality ; universality
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    Notes: Abstract Known differential inequalities for certain ferromagnetic Potts models with pair interactions may be extended to Potts models with many-body interactions. As a major application of such differential inequalities, we obtain necessary and sufficient conditions on the set of interactions of such a Potts model in order that its critical point be astrictly monotonic function of the strengths of interactions. The method yields some ancillary information concerning the equality of certain critical exponents for Potts models; this amounts to a small amount of rigorous universality. These results are achieved in the context of a “Fortuin-Kasteleyn representation” of Potts models with many-body interactions. For such a Potts model, the corresponding random-cluster process is a (random) hypergraph.
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  • 30
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    Journal of statistical physics 85 (1996), S. 297-361 
    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
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    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.
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    Journal of statistical physics 85 (1996), S. 607-637 
    ISSN: 1572-9613
    Keywords: Ising model ; renormalization group pathologies ; Dobrushin uniqueness theorem ; completely analytic potentials
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    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 .
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  • 32
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    Journal of statistical physics 84 (1996), S. 1351-1361 
    ISSN: 1572-9613
    Keywords: Random-cluster model ; quasilocality ; almost sure quasilocality ; tree ; Gibbs measure ; Ising model
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    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.
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    Journal of statistical physics 88 (1997), S. 991-995 
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    Keywords: History of statistical physics ; Ising model
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    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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    Journal of statistical physics 88 (1997), S. 795-805 
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    Keywords: Cellular automata ; Ising model ; voting models ; single sin-flip dynamics ; computational complexity ; parallel computation ; P-completeness
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    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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    Journal of statistical physics 90 (1998), S. 1015-1035 
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    Keywords: Ising model ; mixing conditions ; Basuev region ; boundary conditions ; Glauber dynamics ; exponential relaxation ; spectral gap
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    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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    Journal of statistical physics 98 (2000), S. 1115-1134 
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    Keywords: Ising model ; correlation inequalities ; surface tension ; disorder
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    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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  • 37
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    Journal of statistical physics 1 (1969), S. 71-88 
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    Keywords: Decision theory ; Ising model ; Least square estimation ; Pattern recognition ; Plasmas ; Statistical mechanics
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    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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    Journal of statistical physics 17 (1977), S. 137-152 
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    Keywords: Ising model ; triangular lattice ; corner transfer matrices ; spontaneous magnetization
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    Notes: Abstract Recently, a new technique for investigating the zero-field, eight-vertex model on the square lattice using “corner transfer matrices” was suggested by Baxter. In this paper these ideas are applied to the anisotropic, ferromagnetic, triangular Ising lattice in zero field below its critical temperature. The diagonal form of the corner transfer matrix for the triangular lattice shows essentially the same structure as that for the square Ising lattice. The spontaneous magnetization can be obtained easily and agrees with that previously derived.
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  • 39
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    Journal of statistical physics 19 (1978), S. 349-358 
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    Keywords: Ising model ; lattice statistic ; two-dimensional systems ; critical indices ; transfer matrix ; correlation length
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    Notes: Abstract The critical index valuesγ= 7/4 for the susceptibility andδ=15 for the critical isotherm are derived rigorously for the rectangular Ising ferromagnet with nearest neighbor interactions. The critical indices associated with the Fisher moment definition of the correlation length are obtained asT→T c+. The index of the fluctuation sum definition of critical correlations is obtained.
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    Journal of statistical physics 19 (1978), S. 391-404 
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    Keywords: Helix-coil transition ; heteropolymers ; Ising model ; melting ; random walks
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    Notes: Abstract A method is developed for the calculation of the ground-state melting curves (η o vs.T) for random, infinite heteropolymers. Hereη o is the ground-state value of the fraction of melted linksη (η o ≈ η in the strong cooperativity approximation). It is shown that the differential melting curves (d η/d T vs.T) can have a fine structure in the form of several peaks on the bell-shaped main curve. Positions, magnitudes, and widths of these peaks are estimated. The “accidental” fine structure of melting curves, which is caused by a finite length of the polymer, is briefly discussed.
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  • 41
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    Journal of statistical physics 21 (1979), S. 727-738 
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    Keywords: Ising model ; percolation ; cluster size distribution ; FKG inequalities
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    Notes: Abstract We rigorously prove that the probabilityP n for the origin to belong to a cluster of exactlyn positive spins in thev-dimensional Ising model behaves as exp(−αn(v − 1)/v) in various regions, including in particular the low-temperature positive and negative phases in zero magnetic field.
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  • 42
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    Journal of statistical physics 22 (1980), S. 673-684 
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    Keywords: Block spins ; random field ; mixing random variables ; Ising model
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    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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    Journal of statistical physics 24 (1981), S. 555-586 
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    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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    Journal of statistical physics 25 (1981), S. 361-366 
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    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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  • 45
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    Journal of statistical physics 40 (1985), S. 613-620 
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    Keywords: Ising model ; exact solution ; nonzero magnetic field
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    Notes: Abstract A closed-form expression is obtained for the free energy per site of the Ising model on the triangular lattice in a nonzero magnetic field and with two- and three-site interactions. The solution is valid along a trajectory in the parameter space, and is derived using a method of exact decimation. A criterion determining the validity of the decimation method is also established.
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  • 46
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    Journal of statistical physics 40 (1985), S. 563-575 
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    Keywords: Correlation inequality ; Ising model ; scalar field models
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    Notes: Abstract We present rigorous correlation inequalities for connectedn-point functions in a class of even ferromagnets. The class includes spin-1/2 Ising models and scalar field models with potential functionV which is even and continuously differentiable withV′ convex on [0, ∞). These inequalities are obtained by pushing ahead with the method of Ellis, Monroe, and Newman at its maximum.
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    Journal of statistical physics 45 (1986), S. 135-144 
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    Keywords: Ising model ; phase transitions ; three-component ; honeycomb lattice
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    Notes: Abstract A model three-component system is considered in which the bonds of a honeycomb lattice are covered by rodlike molecules of typesAA, BB, andAB. The ends of molecules near a common lattice site interact with energiesɛ AA,ɛ BB, andɛ AB. The model is equivalent to an Ising model on the 3–12 lattice. Exact results are obtained for the two-phase coexistence curves in the isothermal composition plane.
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  • 48
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    Journal of statistical physics 26 (1981), S. 665-681 
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    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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  • 49
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    Journal of statistical physics 47 (1987), S. 761-771 
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    Keywords: Ising model ; wetting transition ; correlation inequalities
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    Notes: Abstract The phase diagram is analyzed rigorously, and in particular the wetting transition is discussed.
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    Journal of statistical physics 47 (1987), S. 773-799 
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    Keywords: Roughening transition ; equilibrium crystal shape ; ground states ; Ising model ; bcc lattice
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    Notes: Abstract For the Ising model on a bcc lattice we analyze the ground states associated with different interfaces and discuss some consequences on the roughening transition.
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    Journal of statistical physics 47 (1987), S. 979-984 
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    Keywords: Interface ; Ising model ; standard wall ; Brownian sheet
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    Notes: Abstract We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently largeβ. We define the random fieldX L (t, s), 0⩽t, s⩽1, on the interface, and prove that XL(t, s) converges to the Brownian sheet as L→∞ for sufficiently largeβ, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet.
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    Journal of statistical physics 48 (1987), S. 121-134 
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    Keywords: Computational complexity ; Ising model ; monomer-dimer system ; #P-completeness
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    Notes: Abstract The classic problem of counting monomer-dimer arrangements on a two-dimensional lattice is analyzed using techniques from theoretical computer science. Under a certain assumption, made precise in the text, it can be shown that the general problem is computationally intractable. This negative result contrasts with the special case of a system with monomer density zero, for which efficient solutions have been known for some time. A second, much easier result, obtained under the same assumption, is that the partition function of a three-dimensional Ising system is computationally intractable. Again, the negative result contrasts with known efficient techniques for evaluating the partition function of a two-dimensional system.
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  • 53
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    Journal of statistical physics 48 (1987), S. 69-80 
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    Keywords: Lattice statistics ; critical phenomena ; Ising model ; lattice anisotropy ; high-temperature expansion ; inversion relation ; analytical properties
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    Notes: Abstract We combine an exact functional relation, the inversion relation, with conventional high-temperature expansions to explore the analytic properties of the anisotropic Ising model on both the square and simple cubic lattice. In particular, we investigate the nature of the singularities that occur in partially resummed expansions of the partition function and of the susceptibility.
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  • 54
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    Journal of statistical physics 48 (1987), S. 503-511 
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    Keywords: Penrose lattice ; quasicrystal ; Ising model ; percolation ; renormalization group ; phase transition
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    Notes: Abstract The Ising model and the bond percolation model are set up with eight parameters on two-dimensional Penrose lattices. The behavior of their phase transition is studied by the use of a real-space renormalization group method. The resulting critical indices suggest that they belong to the universality class of two-dimensional periodic lattices.
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    Journal of statistical physics 48 (1987), S. 531-538 
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    Keywords: Ising model ; correlation function ; one-dimensional ; inhomogeneous
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    Notes: Abstract We present a new method for the study of a one-dimensional inhomogeneous Ising chain with nonconstant nearest neighbor interactions. The external field required to produce a given magnetization profile is derived exactly. Some properties of the pair direct correlation function are derived. Our findings generalize previous results of Percus.
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    Journal of statistical physics 49 (1987), S. 269-279 
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    Keywords: Ising model ; spontaneous magnetization ; 4–8 lattice ; series expansions
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    Notes: Abstract The spontaneous magnetization of the Ising model on a 4–8 lattice with six different coupling constants and two different magnetic moments is studied. A formula for the spontaneous magnetization is proposed. The result agrees with the exact low-temperature series expansions up to the 12th order.
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  • 57
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    Journal of statistical physics 49 (1987), S. 551-568 
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    Keywords: Stationary nonequilibrium states ; Ising model ; competing temperatures ; nonequilibrium phase transitions
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    Notes: Abstract We study kinetic one- and two-dimensional Ising models whose transition probabilities occur according to two (or more) locally competing temperatures. The model is solved analytically and studied numerically on different assumptions to reveal a variety of stationary nonequilibrium states and phase transitions; we also investigate the system relaxation in some typical cases.
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  • 58
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    Journal of statistical physics 49 (1987), S. 859-865 
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    Keywords: Correlated percolation ; Ising model ; Peierls argument ; minority spins
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    Notes: Abstract We present some new results on the region in theβ-h plane where the + spins percolate for the nearest neighbor Ising model. In particular, it is shown that in high enough dimensionsd there is percolation of the minority spins at inverse temperaturesβ〈β + with someβ +〉βc, for whichβ +/gbc≥1/2log(cd),c a constant.
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  • 59
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    Journal of statistical physics 57 (1989), S. 1049-1058 
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    Keywords: Antiferromagnet ; correlation inequalities ; Ising model
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    Notes: Abstract We prove some inequalities for two-point correlations of Ising antiferromagnets and derive inequalities relating correlations of ferromagnets to correlations of antiferromagnets whose interactions and field strengths have equal magnitudes. The proofs are based on the method of duplicate spin variables introduced by J. Percus and used by several authors to derive correlation inequalities for Ising ferromagnets.
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    Journal of statistical physics 58 (1990), S. 685-706 
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    Keywords: Domain growth kinetics ; Ising model ; six-vertex model
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    Notes: Abstract The time evolution of the Ising model that describes shrinking domains is studied. A singly connected domain of Ising spins, embedded in a sea of the opposite phase, develops atT=0 according to a dynamic rule that does not allow its perimeter to increase. At long enough times the domain disappears; we show that the average lifetime of such a domain is proportional to its area. We also consider theT=0 dynamics of a single infinite quadrant. The area of the quadrant decreases during the time evolution, and we show that the area lost grows linearly with time. We solve a first passage time problem as well. That is, we calculate the average time it takes for the area lost to reach a given value for the first time. Lastly, we map the infinite quadrant model onto a diffusion problem with exclusion in one dimension. This latter problem is mapped onto a critical six-vertex model.
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    Journal of statistical physics 59 (1990), S. 1451-1467 
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    Keywords: Scaling limit ; triviality ; Ising model ; /gf 4 field theory ; upper critical dimension ; bubble diagram ; block variables ; renormalization group
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    Notes: Abstract In the single-phase region (including the critical point) of a nearest-neighbor Ising ferromagnet with zero external field, the block magnetization and energy within the infinite-volume system are, asymptotically for large block size, independent Gaussian variables when the dimensiond exceeds four. For other models, including ones with long-range interactions, a sufficient condition for such triviality of the scaling limit is finiteness of the “bubble quantity”.
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    Journal of statistical physics 60 (1990), S. 167-180 
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    Keywords: Ising model ; surface defects ; surface critical behavior ; conformal invariance ; finite-size scaling
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    Notes: Abstract The surface critical behavior of the two-dimensional Ising model with homogeneous perturbations in the surface interactions is studied on the one-dimensional quantum version. A transfer-matrix method leads to an eigenvalue equation for the excitation energies. The spectrum at the bulk critical point is obtained using anL −1 expansion, whereL is the length of the Ising chain. It exhibits the towerlike structure which is characteristic of conformal models in the case of irrelevant surface perturbations (h s /J s ≠0) as well as for the relevant perturbationh s =0 for which the surface is ordered at the bulk critical point leading to an extraordinary surface transition. The exponents are deduced from the gap amplitudes and confirmed by exact finite-size scaling calculations. Both cases are finally related through a duality transformation.
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  • 63
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    Keywords: Percolation ; “physical clusters” ; Ising model ; Monte Carlo simulation ; finite-size scaling ; Fortuin-Kasteleyn representation ; Swendsen-Wang algorithm
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    Notes: Abstract Finite squareL×L Ising lattices with ferromagnetic nearest neighbor interaction are simulated using the Swendsen-Wang cluster algorithm. Both thermal properties (internal energyU, specific heatC, magnetization 〈|M|〉, susceptibilityχ) and percolation cluster properties relating to the “physical clusters,” namely the Fortuin-Kasteleyn clusters (percolation probability 〈P ∞〉, percolation susceptibilityχ p, cluster size distributionn l) are evaluated, paying particular attention to finite-size effects. It is shown that thermal properties can be expressed entirely in terms of cluster properties, 〈P ∞〉 being identical to 〈|M|〉 in the thermodynamic limit, while finite-size corrections differ. In contrast,χ p differs fromχ even in the thermodynamic limit, since a fluctuation in the size of the percolating net contributes toχ, but not toχ p. NearT c the cluster size distribution has the scaling properties as hypothesized by earlier phenomenological theories. We also present a generalization of the Swendsen-Wang algorithm allowing one to cross over continuously to the Glauber dynamics.
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    Journal of statistical physics 51 (1988), S. 491-499 
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    Keywords: Ising model ; spontaneous magnetization ; layered square lattice ; series expansion
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    Notes: Abstract We have studied the Ising model on a layered square lattice with four different coupling constants and two different magnetic moments. The partition function at zero magnetic field is derived exactly. We propose a formula for the spontaneous magnetization which agrees with the exact low-temperature series expansion up to the 16th order and reduces to the exact result of Au-Yang and McCoy in a special case.
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    Journal of statistical physics 61 (1990), S. 1-50 
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    Keywords: Ising model ; series generation ; series analysis ; critical exponents ; universality
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    Notes: Abstract An implementation of the free-embedding scheme for high-temperature series generation on the body-centered cubic family of lattices in arbitrary dimensiond is, described. Series to order 21 in inverse temperature are tabulated for several scalar field models, both for the magnetic susceptibility and for the second moment of the spin correlation function. The critical behavior of a family of 3-dimensional “double Gaussian” models, which interpolate continuously between the spin-1/2 Ising model and the Gaussian model, is analyzed in detail away from the Gaussian model limit using confluent inhomogeneous secondorder differential approximants. With our best estimate of the correction-to-scaling exponent,θ=0.52±0.03, the leading exponents for the susceptibility and correlation length for this family are consistent with universality and are given byγ=1.237±0.002 and ν=0.630±0.0015, respectively, andη=2−γ/ν=0.0359±0.0007.
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    Journal of statistical physics 61 (1990), S. 121-141 
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    Keywords: Ising model ; superdegenerate ground states ; cluster variation method ; Monte Carlo simulations ; constrained lattice gas
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    Notes: Abstract We investigate the topology of the phase diagram of binary alloys on the fee lattice with first-neighbor antiferromagnetic interactions around the superdegenerate point, where the L10 and L12 phases meet. We treat the system as a “hard-constraint lattice gas,” following a procedure previously described by Lebowitzet al. We perform cluster variation method calculations in theT→0 limit and Monte Carlo simulations directly atT=0 K on the ground states of the superdegenerate point. We find that: (i) there is no disordered phase in the neighborhood of this point; (ii) a phase L′ for which two of the four cubic sublattices have the same average occupancy and each of the two others are different appears between L10 and L12; (iii) the transition L′/L12 is of first order.
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    Journal of statistical physics 61 (1990), S. 161-178 
    ISSN: 1572-9613
    Keywords: Critical wetting ; Ising model ; Monte Carlo simulations ; finite-size scaling
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    Notes: Abstract The Ising square lattice with nearest-neighbor exchangeJ〉0 and a free surface at which a boundary magnetic fieldH 1 acts has a second-order wetting transition. We study the surface excess magnetization and the susceptibility ofL×M lattices by Monte Carlo simulation and probe the critical behavior of this wetting transition, applying finite-size scaling methods. For the cases studied, the results are not consistent with the presumably exactly known values of the critical exponents, because the asymptotic critical region has not yet been reached. Implication of our results for critical wetting in three dimensions and for the application of the present model to adsorbed wetting layers at surface steps are briefly discussed.
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    Journal of statistical physics 61 (1990), S. 241-252 
    ISSN: 1572-9613
    Keywords: Ising model ; zero-temperature limit ; sharp transition ; fluctuations ; criticality
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    Topics: Physics
    Notes: Abstract In the limit as the volume grows and the temperature vanishes, it is shown that the one-dimensional nearest neighbor ferromagnetic Ising model presents a sharp transition between two different regimes. Fluctuations are studied in one of these regimes and also in the critical case.
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    Journal of statistical physics 52 (1988), S. 815-827 
    ISSN: 1572-9613
    Keywords: 2D spin system ; Ising model ; linear defect ; spin correlation
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    Topics: Physics
    Notes: Abstract The dispersion expansion for the spin correlation function in the two-dimensional Ising model with linear defects aboveT c is derived. The asymptotic behavior is computed by a steepest descent analysis. The lattice is divided into four domains with different asymptotic behaviors. In particular, the correlation length inside certain domains is a function of the defect.
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    Journal of statistical physics 57 (1989), S. 595-629 
    ISSN: 1572-9613
    Keywords: Neutron scattering function ; shear viscosity ; bulk viscosity ; thermal conductivity ; Green-Kubo integrand ; hard-sphere fluid ; short-time expansion
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    Topics: Physics
    Notes: Abstract The short-time behavior of the coherent intermediate scattering function for a fluid of hard-sphere particles is calculated exactly through ordert 4, and the other hydrodynamic correlation functions are calculated exactly through ordert 2. It is shown that for all of the correlation functions considered the Enskog theory gives a fair approximation. Also, the initial time behavior of various Green-Kubo integrands is studied. For the shear-viscosity integrand it is found that at densitynσ3=0.837 the prediction of the Enskog theory is 32% too low. The initial value of the bulk viscosity integrand is nonzero, in contrast to the Enskog result. The initial value of the thermal conductivity integrand at high densities is predicted well by Enskog theory.
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    Journal of statistical physics 78 (1995), S. 575-584 
    ISSN: 1572-9613
    Keywords: Ising model ; correlation functions ; spontaneous magnetization ; Toeplitz determinants ; Szegö limit theorems ; Toeplitz operators
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    Topics: Physics
    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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    Journal of statistical physics 78 (1995), S. 893-916 
    ISSN: 1572-9613
    Keywords: Dynamic critical phenomena ; disordered spin systems ; Ising model ; finite size ; scaling
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    Topics: Physics
    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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    Journal of statistical physics 79 (1995), S. 25-42 
    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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    Journal of statistical physics 73 (1993), S. 723-749 
    ISSN: 1572-9613
    Keywords: Ising model ; layered systems ; phase diagram ; interlayer coupling ; mean-field theory ; renormalization group ; scaling theory ; Monte Carlo simulation
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    Notes: Abstract The statistical mechanics of two Ising ferromagnetic planes coupled by a local interlayer two-spin interaction have been studied by means of a variety of calculational methods, including different mean-field approximations, Migdal-Kadanoff-type renormalization-group techniques, scaling theory, as well as numerical Monte Carlo simulation techniques. The phase diagram has been derived as a function of the interlayer coupling strength. Furthermore, various thermodynamic variables have been determined, including the interlayer correlation function, which is proportional to the interplanar force. It is found that a Migdal-Kadanoff renormalization with a decimation procedure which involves the interlayer coupling in an appropriate fashion provides an accurate description of the phase diagram and that a mean-field description provides a good description of the phase diagram and the interplanar force, except for very low interlayer coupling strengths.
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    Journal of statistical physics 74 (1994), S. 411-432 
    ISSN: 1572-9613
    Keywords: Large deviations ; Ising model ; Wulff construction
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    Topics: Physics
    Notes: Abstract We show that a lower large-deviation bound for the block-spin magnetization in the 2D Ising model can be pushed all the way forward toward its correct “Wulff” value for all β〉βc.
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    Journal of statistical physics 82 (1996), S. 87-113 
    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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    Journal of statistical physics 84 (1996), S. 655-696 
    ISSN: 1572-9613
    Keywords: Ising model ; Glauber dynamics ; relaxation time
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    Topics: Physics
    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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    Journal of statistical physics 75 (1994), S. 409-506 
    ISSN: 1572-9613
    Keywords: Stochastic dynamics ; Ising model ; next nearest neighbor interaction ; metastability ; crystal growth ; first excursion
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    Topics: Physics
    Notes: Abstract Nucleation from a metastable state is studied for an Ising ferromagnet with nearest and next nearest neighbor interaction and at very low temperatures. The typical escape path is shown to follow a sequence of configurations with a growing droplet of stable phase whose shape is determined by dynamical considerations and differs significantly from the equilibrium shape corresponding to the instantaneous volume.
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    Journal of statistical physics 86 (1997), S. 149-164 
    ISSN: 1572-9613
    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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    Journal of statistical physics 90 (1998), S. 211-226 
    ISSN: 1572-9613
    Keywords: Ising model ; stochastic dynamics ; metastability ; nucleation
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    Topics: Physics
    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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    Journal of statistical physics 90 (1998), S. 1051-1059 
    ISSN: 1572-9613
    Keywords: Ising model ; Peierls contour ; low-temperature expansion ; high dimension
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    Topics: Physics
    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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    Journal of statistical physics 92 (1998), S. 1203-1208 
    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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    Journal of statistical physics 93 (1998), S. 33-78 
    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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    Topics: Physics
    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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    Journal of statistical physics 94 (1999), S. 299-320 
    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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    Journal of statistical physics 94 (1999), S. 321-345 
    ISSN: 1572-9613
    Keywords: dynamical triangulations ; quenched disorder ; Ising model
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    Topics: Physics
    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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    Journal of statistical physics 96 (1999), S. 135-167 
    ISSN: 1572-9613
    Keywords: statistical entropy ; multiparticle correlations ; cumulant expansion ; lattice gases ; Ising model
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    Topics: Physics
    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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  • 87
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    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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    Journal of statistical physics 98 (2000), S. 131-244 
    ISSN: 1572-9613
    Keywords: Ising model ; boundary conditions ; renormalization group ; free boson ; conformal invariance ; critical phenomena
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    Topics: Physics
    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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    Journal of statistical physics 98 (2000), S. 321-345 
    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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    Topics: Physics
    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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    Journal of statistical physics 99 (2000), S. 691-705 
    ISSN: 1572-9613
    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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    Il nuovo cimento della Società Italiana di Fisica 16 (1994), S. 1679-1683 
    ISSN: 0392-6737
    Keywords: Thermodynamic properties ; thermal conductivity ; Methods of crystals growth and purification ; Phase diagrams of other materials ; Conference proceedings
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    Topics: Physics
    Notes: Summary In this work the thermal conditions required for single-crystal growth in RBa2Cu3O7−x systems (R=Y or rare earths apart from Ce and Tb) have been systematically revised in order to improve the size of crystals obtainable by the flux method. Large single crystals of NdBCO, SmBCO and EuBCO have been actually obtained and characterized by XRD, oxygen content and electrical resistivity.
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    Il nuovo cimento della Società Italiana di Fisica 16 (1994), S. 1863-1869 
    ISSN: 0392-6737
    Keywords: Thermodynamic properties ; thermal conductivity ; Conference proceedings
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    Topics: Physics
    Notes: Summary Superconducting powders with nominal composition Bi1.84Pb0.34Sr1.91Ca2.03Cu3.06Ox were prepared by two different routes: by solid-state reaction of the respective oxides and carbonates and by pyrolysis of organic precursors. Highly dense superconducting specimens characterized by textured microstructure were prepared by hot pressing. The thermal-expansion coefficients of different typologies of samples were measured by dilatometric tests in both directions parallel and perpendicular to the pressure application direction. Structural rearrangements occurring during thermal treatments were studied. As regards mechanical characterization, microhardness, flexural strength and fracture toughness were evaluated and related to the microstructure anisotropic degree of the sample.
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    European biophysics journal 16 (1988), S. 39-44 
    ISSN: 1432-1017
    Keywords: Lipid monolayers ; phase transitions ; Ising model
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    Topics: Biology , Physics
    Notes: Abstract A microscopic model of a lipid monolayer is proposed. It includes, within a single scheme, the following factors which are considered to be essential in phase transitions in lipid systems: formation of gauche rotamers, interactions between polar heads, interactions between hydrocarbon chains (depending on their conformation) and changes in the energy of the system due to a directional ordering of the chains. Phase diagrams are constructed and discussed and it is shown how the phase diagrams are modified by alterations of these parameters and the length of the hydrocarbon chains.
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    Journal of nanoparticle research 2 (2000), S. 199-204 
    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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    Water, air & soil pollution 98 (1997), S. 345-359 
    ISSN: 1573-2932
    Keywords: thermal conductivity ; thermal diffusivity ; waste rock
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    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract In situ determinations of thermal conductivity of waste rock dumps at three mine sites: Aitik, Sweden; Kelian, Indonesia; and Heath Steele, Canada are described. Measurements were carried out at various locations and depths at each site. The estimated thermal conductivities range from 0.62 to 1.63 W m−1K−1 with an average of 1.21±0.27 W m−1K−1 for the waste rock pile at the Aitik site, 1.04 to 1.25 W m−1K−1 with an average value of 1.17(0.11 W m−1K−1 for the Heath Steele site, and 1.57 to 2.08 W m−1K−1 with an average value of 1.89±0.21 W m−1K−1 for the Kelian site. The higher average thermal conductivity at the Kelian site could be attributed to higher moisture content in the waste rock pile because of high rainfall at this site. Thermal diffusivity was also evaluated at a region of the Aitik waste rock dump where the thermal conductivity was also determined using measured temperature profiles. The thermal diffusivity value determined this way was (5.75±0.75)×10−7m2s−1, consistent with that calculated from the thermal conductivity values determined for the same location.
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    Applied mathematics and mechanics 18 (1997), S. 211-220 
    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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    Rheologica acta 35 (1996), S. 103-109 
    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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  • 98
    ISSN: 1573-0689
    Keywords: Neural networks ; primate visual cortex ; pattern formation model ; Langevin equation ; Ising model
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    Topics: Biology , Physics
    Notes: Abstract We present a neural network model for the formation of ocular dominance stripes on primate visual cortex and examine the generic phase behavior and dynamics of the model. The dynamical equation of ocular dominance development can be identified with a class of Langevin equations with a nonconserved order parameter. We first set up and examine an Ising model with long-range interactions in an external field, which is equivalent to the model described by the Langevin equation. We use both mean-field theory and Monte-Carlo simulations to study the equilibrium phase diagram of this equivalent Ising model. The phase diagram comprises three phases: a striped phase, a hexagonal ‘bubble’ phase, and a uniform paramagnetic phase. We then examine the dynamics of the striped phase by solving the Langevin equation both numerically and by singular perturbation theory. Finally, we compare the results of the model with physiological data. The typical striped structure of the ocular dominance columns corresponds to the zero-field configurations of the model. Monocular deprivation can be simulated by allowing the system to evolve in the absence of an external field at early times and then continuing the simulation in the presence of an external field. The physical and physiological applications of our model are discussed in the conclusion.
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    Journal of superconductivity 12 (1999), S. 497-500 
    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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    Electronic Resource
    Springer
    Journal of superconductivity 7 (1994), S. 323-329 
    ISSN: 1572-9605
    Keywords: High-T c superconductors ; thermal conductivity ; scattering rate
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Physics
    Notes: Abstract The thermal conductivityК of hole-doped Cu-O plane high-T c perovskites exhibits a dramatic increase belowT c which results in a pronounced peak nearT c /2. The origin of this peak was initially thought to arise from an enhancement in the mean-free path of phonons as the charge carriers undergo condensation. Indeed, excellent fits to the data can be obtained with physically reasonable parameters using the conventional theory of lattice conduction in superconductors. In contrast, a recently observed sharp decrease in the quasiparticle scattering rate of YBCO single crystals belowT c has motivated proposals for an electronic origin of the thermal conductivity peak. We shall critically examine experimental evidence and highlight relative advantages and shortcomings of the two contrasting interpretations. Furthermore, we shall draw attention to recently available data on the relaxation time of out-of-equilibrium carriers in Cu-O superconductors obtained using pump-probe femtosecond laser studies and what new light they shed on the controversy.
    Type of Medium: Electronic Resource
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