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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Letters in mathematical physics 46 (1998), S. 207-218 
    ISSN: 1573-0530
    Schlagwort(e): Ising model ; boundary conditions ; Boltzmann weights.
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: 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
    Digitale Medien
    Digitale Medien
    Springer
    Letters in mathematical physics 37 (1996), S. 137-143 
    ISSN: 1573-0530
    Schlagwort(e): 82B20 ; 82B26 ; 82B43 ; Bethe lattice ; FK representation ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Physik
    Notizen: 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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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 78 (1995), S. 285-297 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Lee-Yang zeros ; edge singularities ; nonperiodic systems ; phase transitions ; gap labeling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 78 (1995), S. 731-757 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; renormalization group ; finite-size conditions ; critical point
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 78 (1995), S. 1311-1324 
    ISSN: 1572-9613
    Schlagwort(e): Random-cluster model ; Ising model ; Potts model ; comparison inequality ; BK inequality ; FKG inequality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 78 (1995), S. 1131-1138 
    ISSN: 1572-9613
    Schlagwort(e): Kac potential ; Ising model ; critical fluctuations ; Euclidean field theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 74 (1994), S. 903-908 
    ISSN: 1572-9613
    Schlagwort(e): Dynamic critical exponent ; Ising model ; damage spreading
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 82 (1996), S. 1299-1326 
    ISSN: 1572-9613
    Schlagwort(e): Cluster algorithms ; computational complexity ; diffusion-limited aggregation ; Ising model ; Metropolis algorithm ; P-completeness
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 75 (1994), S. 67-121 
    ISSN: 1572-9613
    Schlagwort(e): Potts model ; Ising model ; random-cluster process ; critical temperature ; critical exponent ; differential inequality ; universality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 85 (1996), S. 297-361 
    ISSN: 1572-9613
    Schlagwort(e): 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
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 11
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 85 (1996), S. 607-637 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; renormalization group pathologies ; Dobrushin uniqueness theorem ; completely analytic potentials
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 12
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 84 (1996), S. 1351-1361 
    ISSN: 1572-9613
    Schlagwort(e): Random-cluster model ; quasilocality ; almost sure quasilocality ; tree ; Gibbs measure ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 13
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 88 (1997), S. 991-995 
    ISSN: 1572-9613
    Schlagwort(e): History of statistical physics ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 14
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 88 (1997), S. 795-805 
    ISSN: 1572-9613
    Schlagwort(e): Cellular automata ; Ising model ; voting models ; single sin-flip dynamics ; computational complexity ; parallel computation ; P-completeness
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 15
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 90 (1998), S. 1015-1035 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; mixing conditions ; Basuev region ; boundary conditions ; Glauber dynamics ; exponential relaxation ; spectral gap
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 16
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 98 (2000), S. 1115-1134 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; correlation inequalities ; surface tension ; disorder
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 17
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 58 (1990), S. 685-706 
    ISSN: 1572-9613
    Schlagwort(e): Domain growth kinetics ; Ising model ; six-vertex model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 18
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 59 (1990), S. 1451-1467 
    ISSN: 1572-9613
    Schlagwort(e): Scaling limit ; triviality ; Ising model ; /gf 4 field theory ; upper critical dimension ; bubble diagram ; block variables ; renormalization group
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 19
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 60 (1990), S. 167-180 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; surface defects ; surface critical behavior ; conformal invariance ; finite-size scaling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 20
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 60 (1990), S. 585-618 
    ISSN: 1572-9613
    Schlagwort(e): Percolation ; “physical clusters” ; Ising model ; Monte Carlo simulation ; finite-size scaling ; Fortuin-Kasteleyn representation ; Swendsen-Wang algorithm
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 21
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 1-50 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; series generation ; series analysis ; critical exponents ; universality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 22
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 121-141 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; superdegenerate ground states ; cluster variation method ; Monte Carlo simulations ; constrained lattice gas
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 23
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 161-178 
    ISSN: 1572-9613
    Schlagwort(e): Critical wetting ; Ising model ; Monte Carlo simulations ; finite-size scaling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 24
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    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 241-252 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; zero-temperature limit ; sharp transition ; fluctuations ; criticality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 25
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    Digitale Medien
    Springer
    Journal of statistical physics 78 (1995), S. 575-584 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; correlation functions ; spontaneous magnetization ; Toeplitz determinants ; Szegö limit theorems ; Toeplitz operators
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 26
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 78 (1995), S. 893-916 
    ISSN: 1572-9613
    Schlagwort(e): Dynamic critical phenomena ; disordered spin systems ; Ising model ; finite size ; scaling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 27
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 79 (1995), S. 25-42 
    ISSN: 1572-9613
    Schlagwort(e): Renormalization group ; decimation ; non-Gibbsianness ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 28
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 73 (1993), S. 723-749 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; layered systems ; phase diagram ; interlayer coupling ; mean-field theory ; renormalization group ; scaling theory ; Monte Carlo simulation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 29
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 74 (1994), S. 411-432 
    ISSN: 1572-9613
    Schlagwort(e): Large deviations ; Ising model ; Wulff construction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 30
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 82 (1996), S. 87-113 
    ISSN: 1572-9613
    Schlagwort(e): Onsager's algbera ; loop algebras ; Ising model ; integrability
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 31
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 84 (1996), S. 655-696 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Glauber dynamics ; relaxation time
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 32
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 75 (1994), S. 409-506 
    ISSN: 1572-9613
    Schlagwort(e): Stochastic dynamics ; Ising model ; next nearest neighbor interaction ; metastability ; crystal growth ; first excursion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 33
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 86 (1997), S. 149-164 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Gibbs measures ; large-deviation principle
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 34
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 90 (1998), S. 211-226 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; stochastic dynamics ; metastability ; nucleation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 35
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 90 (1998), S. 1051-1059 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Peierls contour ; low-temperature expansion ; high dimension
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 36
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 92 (1998), S. 1203-1208 
    ISSN: 1572-9613
    Schlagwort(e): Loop model ; criticality ; universality ; 3–12 lattice ; self-avoiding walk ; connective constant ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 37
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 93 (1998), S. 33-78 
    ISSN: 1572-9613
    Schlagwort(e): Random external field ; Ising model ; Gibbs states ; ground states ; Bethe lattice ; residual entropy ; dipole configurations ; Griffiths singularities
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 38
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 94 (1999), S. 299-320 
    ISSN: 1572-9613
    Schlagwort(e): wetting ; surface tension ; rough surfaces ; Wenzel's law ; semi-infinite systems ; Ising model ; cluster expansions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 39
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 94 (1999), S. 321-345 
    ISSN: 1572-9613
    Schlagwort(e): dynamical triangulations ; quenched disorder ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 40
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 96 (1999), S. 135-167 
    ISSN: 1572-9613
    Schlagwort(e): statistical entropy ; multiparticle correlations ; cumulant expansion ; lattice gases ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 41
    ISSN: 1572-9613
    Schlagwort(e): renormalization group ; Gibbsianness ; finite-size conditions ; complete analyticity ; strong mixing ; equivalence of ensembles ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 42
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 98 (2000), S. 131-244 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; boundary conditions ; renormalization group ; free boson ; conformal invariance ; critical phenomena
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 43
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 98 (2000), S. 321-345 
    ISSN: 1572-9613
    Schlagwort(e): statistical mechanics ; variance reduction ; Monte Carlo algorithms ; Metropolis algorithm ; statistical estimators ; Ising model ; histogram methods ; transition probabilities
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 44
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 99 (2000), S. 691-705 
    ISSN: 1572-9613
    Schlagwort(e): Monte Carlo methods ; Ising model ; computational physics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: 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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  • 45
    ISSN: 1573-0689
    Schlagwort(e): Neural networks ; primate visual cortex ; pattern formation model ; Langevin equation ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Physik
    Notizen: 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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  • 46
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 58 (1990), S. 141-157 
    ISSN: 1572-9613
    Schlagwort(e): Lattice gas ; cellular automata ; microcanonical ensemble ; Ising model ; deterministic dynamics ; spin glass
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We introduce a lattice gas for particles with discrete momenta (1, 0, −1) and local deterministic microdynamics, which exactly reproduces Creutz's microcanonical algorithm for the ferromagnetic Ising model. However, because of the manifest gauge invariance of our variables, both the Ising ferromagnetic and spin-glass systems share precisely the same dynamics with different initial conditions. Additional conservation laws in the 1D Ising case result in a completely integrable system in the limit of zero or unbounded demon energy cutoff. Numerical investigations of ergodicity are presented for the pure Ising lattice gas in one and two dimensions.
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  • 47
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 60 (1990), S. 347-361 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; phase transitions ; double critical point ; three-component
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A model is considered in which the bonds of a lattice are covered by rodlike molecules. Neighboring molecular ends interact with orientation-dependent interactions. The model exhibits closed -loop phase diagrams and double critical points. Exact coexistence surfaces are calculated for the model on the Bethe, honeycomb, and square lattices. The nature of the doubling of the critical exponentβ near a double critical point is calculated. The behavior of the critical line in the neighborhood of a double critical point is calculated exactly.
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  • 48
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 60 (1990), S. 851-861 
    ISSN: 1572-9613
    Schlagwort(e): Nucleation ; metastability ; Ising model ; Metropolis ; Swendsen-Wang ; spinodal point ; critical dynamics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The behavior of the metastable nearest neighbor Ising model governed by Swendsen-Wang dynamics (SW) is investigated ind=2. The results are compared to those obtained in standard Metropolis dynamics. Both the SW and Metropolis systems are observed to decay from the metastable state via the formation of nucleating droplets. Nucleation rates are measured and found to agree with those predicted by classical nucleation theory. The growth rates of the droplets are observed to differ between the two dynamics. In addition, the dynamic critical exponentz is measured in a mean-field (Curie-Weiss) metastable Ising model at the spinodal. It is found that for SW dynamics,z=2. Since this is the same value as that obtained in the Metropolis case, this result shows that SW does not change the dynamical universality class at the spinodal.
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  • 49
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 891-902 
    ISSN: 1572-9613
    Schlagwort(e): Nucleation ; spinodal ; metastability ; mean-field ; percolation ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Properties of metastable long-range Ising models (LRIMs) are studied for deep quenches near the mean-field spinodal with Monte Carlo simulations using Glauber dynamics. The theory of spinodal-assisted nucleation is found to agree well with the data. Nucleating droplets are shown to have the same structure as large clusters in random long-range bond percolation.
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  • 50
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 913-921 
    ISSN: 1572-9613
    Schlagwort(e): Multifractality ; Ising model ; hierarchical lattices ; magnetization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A new approach is applied to show that the local magnetization of the ferromagnetic Ising model on hierarchical lattices has a multifractal structure at the critical point. Thef(α) function characterizing its multifractality is presented and discussed for the diamond hierarchical lattice. Distinct exact critical exponents for the average magnetization and for the local magnetization of the deepest sites are found. The average magnetization (as function of the temperature) is also calculated. The critical exponent of the susceptibility is estimated using finite-size scale arguments.
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  • 51
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 62 (1991), S. 117-133 
    ISSN: 1572-9613
    Schlagwort(e): Monte Carlo algorithms ; Ising model ; approach to equilibrium
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We present rigorous results on the exponential convergence to equilibrium for the Swendsen-Wang stochastic dynamics for thed-dimensional Ising ferromagnet with external magnetic fieldh in the thermodynamic limit. We consider various situations, mainly in the low-temperature regime, in which boundary conditions are homogeneous and parallel or opposite to the external field. In the latter case we relate directly the tunneling from the metastable phase to the stable one with the exponential convergence to equilibrium.
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  • 52
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; random cluster dynamics ; stable and metastable phases ; nucleation ; critical droplets
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider the Swendsen-Wang dynamics for the two-dimensional Ising model at low temperature in the presence of a small negative magnetic fieldh and with plus boundary conditions at the boundary of an arbitrarily large square. We analyze in detail the tunneling from the metastable phase to the stable one. In particular, we obtain an upper bound on the tunneling timet β by explicitly constructing paths in the space of spin configurations that drive the system from the metastable phase to the stable one. In our analysis the transition takes place through the formation of droplets of the right phase inside the wrong one with side greater than a certain critical valuel c . The values of the tunneling time and ofl c coincide with those found for a single-spin-flip dynamics in finite volume by Jordao-Neves and Schonmann.
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  • 53
    Digitale Medien
    Digitale Medien
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    Journal of statistical physics 62 (1991), S. 463-472 
    ISSN: 1572-9613
    Schlagwort(e): Nucleation ; spinodal ; metastability ; mean-field ; Monte Carlo ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Conventional theories of nucleation predict that the metastable state has an average lifetime which monotonically decreases as the system is quenched further from the condensation point. However, theories based on the coarsegrained Ginzburg-Landau free energy functional seem to indicate that for systems above six dimensions there is a sharp spinodal dividing the metastable and unstable regimes where the lifetime of the metastable state diverges. Monte Carlo simulations are used to investigate this discrepency. Both nucleation rates and bulk susceptibility measurements seem to support the prediction of the Ginzburg-Landau theories.
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  • 54
    Digitale Medien
    Digitale Medien
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    Journal of statistical physics 63 (1991), S. 1077-1096 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; interfaces ; finite-size effects ; Monte Carlo
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider a two-dimensional Ising cylinder of circumferenceM and heightN, with a floating interface introduced by the appropriate boundary conditions. An exact analysis of the finite-size effects in surface tension is given and the scaling function for all temperatures is calculated. The results are compared with the Monte Carlo data of Mon and Jasnow.
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  • 55
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 63 (1991), S. 1097-1111 
    ISSN: 1572-9613
    Schlagwort(e): Wetting ; random surface ; Ising model ; monolayer
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We continue our analysis of the phase diagram of a discrete random surface, with no “downward fingers,” lying above a flat two-dimensional substrate. The surface is closely related to the 2D Ising model and its free energy is exactly solvable in much (but not all) of the phase diagram. There is a transition at temperatureT w from a high-T infinite height or wet phase to a low-T finite height or partially wet phase. Previously it was shown that when a parameterb, related to the contact interaction, is positive,T w is independent ofb and there is a logarithmic specific heat divergence asT w is approached fromeither side. Here we show that forb〈0,T w does depend onb and there isno thermodynamic singularity from the wet phase. The partially wet phases forb⩽0 andb〉0 differ in the absence or presence of a monolayer covering the entire substrate; this results in a first-order transition across the lineb=0,T〈T w.
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  • 56
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 65 (1991), S. 291-316 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Potts model ; directed self-avoiding walks ; Dirac propagator ; conformational statistics of semiflexible polymers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A new discretized version of the Dirac propagator ind space and one time dimensions is obtained with the help of the 2d-state, one-dimensional Potts model. The Euclidean version of this propagator describes all conformational properties of semiflexible polymers. It also describes all properties of fully directed self-avoiding walks. The case of semiflexible copolymers composed of a random sequence of fully flexible and semirigid monomer units is also considered. As a by-product, some new results for disordered one-dimensional Ising and Potts models are obtained. In the case of the Potts model the nontrivial extension of the results to higher dimensions is discussed briefly.
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  • 57
    Digitale Medien
    Digitale Medien
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    Journal of statistical physics 66 (1992), S. 139-164 
    ISSN: 1572-9613
    Schlagwort(e): Random-field ; Ising model ; Gibbs states ; self-averaging
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract An approach to the definition of infinite-volume Gibbs states for the (quenched) random-field Ising model is considered in the case of a Curie-Weiss ferromagnet. It turns out that these states are random quasi-free measures. They are random convex linear combinations of the free product-measures “shifted” by the corresponding effective mean fields. The conditional self-averaging property of the magnetization related to this randomness is also discussed.
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  • 58
    Digitale Medien
    Digitale Medien
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    Journal of statistical physics 66 (1992), S. 867-883 
    ISSN: 1572-9613
    Schlagwort(e): Critical phenomena ; disordered spin systems ; Ising model ; field-theoretic approach in general dimensions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Critical exponents of weakly dilute Ising-like systems are computed for non-integer space dimensionalities in the range 2〈/d⩽4. The calculations are performed in the framework of the Callan-Symanzik field-theoretic approach. Two-loop renormalization group functions are obtained as renormalized perturbation theory series expansions directly in noninteger dimensions. The values of the critical exponents are estimated with the use of the two-variable Borel resummation method.
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  • 59
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    Journal of statistical physics 66 (1992), S. 1155-1163 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Kawasaki dynamics ; surface tension
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We present results of a stochastic simulation which determines the shape of a liquid drop, subject to gravity, on a wall. The system is modeled using an Ising model in a field gradient, with Kawasaki dynamics governing the time dependence. We can locate a phase transition between a hanging and a sliding phase with high precision and determine its critical exponents.
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  • 60
    Digitale Medien
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    Journal of statistical physics 66 (1992), S. 1225-1244 
    ISSN: 1572-9613
    Schlagwort(e): Density functionals ; energy functionals ; Ising model ; scaling theory ; criticality ; surfaces ; interfaces ; microcanonical ; one-dimensional
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Free-energy functionals suitable for describing realistic, nonuniform systems near criticality are discussed with emphasis on the advantages of a local formalism. It is proposed to investigatemicro canonical functionals in which both the usual order-parameter (or magnetization) density m(r)and the local energy density ɛ(r), which has independent critical fluctuations, are employed. This approach is tested by an exact calculation of the microcanonical functional ℒ[{m}, {ɛ}] in the continuum limit for a one-dimensional Ising model. Remarkably, the microcanonical functional is found to be local irrespective of the proximity to the critical point (located at zero temperature and zero field). Furthermore, its form relates closely to the scaling postulate advanced earlier by de Gennes and Fisher and displays features of conformal covariance.
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  • 61
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    Journal of statistical physics 69 (1992), S. 55-65 
    ISSN: 1572-9613
    Schlagwort(e): Percolation ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We study the critical behavior of certain two-parameter families of correlated percolation models related to the Ising model on the triangular and square lattices, respectively. These percolation models can be considered as interpolating between the percolation model given by the + and − clusters and the Fortuin-Kasteleyn correlated percolation model associated to the Ising model. We find numerically on both lattices a two-dimensional critical region in which the expected cluster size diverges, yet there is no percolation.
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  • 62
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    Journal of statistical physics 70 (1993), S. 1391-1400 
    ISSN: 1572-9613
    Schlagwort(e): Phase transition ; antiferromagnet ; Gibbs state ; free energy ; pressure ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider a spin system with nearest-neighbor antiferromagnetic pair interactions in a two-dimensional lattice. We prove that the free energy of this system is differentiable with respect to the uniform external fieldh, for all temperatures and allh. This implies the absence of a first-order phase transition in this system.
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  • 63
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    Journal of statistical physics 78 (1995), S. 7-16 
    ISSN: 1572-9613
    Schlagwort(e): Statistical mechanics ; lattice models ; Ising model ; solvable models ; integrable systems ; Yang-Baxter relations
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract There is now a whole field in mathematical physics concerned with solvable models in statistical mechanics, field theory, and related areas. We indicate the influence that Onsager's solution of the planar Ising model has had, and continues to have, on this field.
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  • 64
    Digitale Medien
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    Journal of statistical physics 81 (1995), S. 837-842 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; staggered field ; metastable state
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We report a Monte Carlo simulation of the layered Ising antiferromagnet under an external magnetic field. We show that under a staggered field, there occurs a phase transition from a metastable state which follows a Vogel-Fulcher law. For a staggered intrasublattice interaction a similar situation occurs.
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  • 65
    Digitale Medien
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    Journal of statistical physics 83 (1996), S. 867-905 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Wulff shape ; large deviations ; boundary effects
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We continue our study of the behavior of the two-dimensional nearest neighbor ferromagnetic Ising model under an external magnetic fieldh, initiated in our earlier work. We strengthen further a result previously proven by Martirosyan at low enough temperature, which roughly states that for finite systems with (−)-boundary conditions under a positive external field, the boundary effect dominates in the system if the linear size of the system is of orderB/h withB small enough, while ifB is large enough, then the external field dominates in the system. In our earlier work this result was extended to every subcritical value of the temperature. Here for every subcritical value of the temperature we show the existence of a critical valueB 0 (T) which separates the two regimes specified above. We also find the asymptotic shape of the region occupied by the (+)-phase in the second regime, which turns out to be a “squeezed Wulff shape”. The main step in our study is the solution of the variational problem of finding the curve minimizing the Wulff functional, which curve is constrained to the unit square. Other tools used are the results and techniques developed to study large deviations for the block magnetization in the absence of the magnetic field, extended to all temperatures below the critical one.
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  • 66
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    Journal of statistical physics 84 (1996), S. 1077-1093 
    ISSN: 1572-9613
    Schlagwort(e): Gibbs states ; ground states ; residual entropy ; random field ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider the random Gibbs field formalism for the ferromagnetic ID dichotomous random-field Ising model as the simplest example of a quenched disordered system. We prove that for nonzero temperatures the Gibb state is unique for any realization of the external field. Then we prove that asT→0, the Gibbs state converges to a limit, a ground state, for almost all realizations of the external field. The ground state turns out to be a probability measure concentrated on an infinite set of configurations, and we give a constructive description of this measure.
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  • 67
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    Journal of statistical physics 75 (1994), S. 757-763 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; cellular automata ; critical exponents
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Static critical exponents for the two-dimensional Ising model are computed on a cellular automaton. The analysis of the data within the framework of the finite-size scaling theory reproduces their well-established values.
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  • 68
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    Journal of statistical physics 76 (1994), S. 347-360 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; lattice relaxation ; phonon ; order-disorder transition
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Lattice models such as Ising or Potts models are very often successfully applied to order-disorder phenomena in solids (e.g., for alloys) or on surfaces (e.g., for physisorption). In this contribution it is shown how to derive such models from a microscopic Hamiltonian in the framework of classical statistical mechanics. Both structural relaxations and thermal fluctuations can be incorporated within the (temperature-dependent) parameters of the lattice model.
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  • 69
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    Journal of statistical physics 76 (1994), S. 1179-1246 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; phase coexistence region
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider a Glauber dynamics reversible with respect to the two-dimensional Ising model in a finite square of sideL, in the absence of an external field and at large inverse temperature β. We first consider the gap in the spectrum of the generator of the dynamics in two different cases: with plus and open boundary conditions. We prove that, when the symmetry under global spin flip is broken by the boundary conditions, the gap is much larger than the case in which the symmetry is present. For this latter we compute exactly the asymptotics of −(1/βL) log(gap) asL→∞ and show that it coincides with the surface tension along one of the coordinate axes. As a consequence we are able to study quite precisely the large deviations in time of the magnetization and to obtain an upper bound on the spin-spin time correlation in the infinite-volume plus phase. Our results establish a connection between the dynamical large deviations and those of the equilibrium Gibbs measure studied by Shlosman in the framework of the rigorous description of the Wulff shape for the Ising model. Finally we show that, in the case of open boundary conditions, it is possible to rescale the time withL in such a way that, asL→∞, the finite-dimensional distributions of the time-rescaled magnetization converge to those of a symmetric continuous-time Markov chain on the two-state space {−m *(β),m *(β)},m *(β) being the spontaneous magnetization. Our methods rely upon a novel combination of techniques for bounding from below the gap of symmetric Markov chains on complicated graphs, developed by Jerrum and Sinclair in their Markov chain approach to hard computational problems, and the idea of introducing “block Glauber dynamics” instead of the standard single-site dynamics, in order to put in evidence more effectively the effect of the boundary conditions in the approach to equilibrium.
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  • 70
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    Journal of statistical physics 76 (1994), S. 1505-1510 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; long-range interactions ; critical temperature
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We present upper bounds on the critical temperature of one-dimensional Ising models with long-range,l/n α interactions, where 1〈α≦2. In particular for the often studied case of α=2 we have an upper bound onT c which is less than theT c found by a number of approximation techniques. Also for the case where α is small, such as α=1.1, we obtain rigorous bounds which are extremely close, within 1.0%, to those found by approximation methods.
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  • 71
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    Journal of statistical physics 77 (1994), S. 77-87 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Monte Carlo dynamics ; spontaneous gauge symmetry breaking
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The hydrodynamic regime of superfluids is dominated by a Goldstone mode corresponding to a spontaneously brokenU(1) symmetry. In this article we map the Kawasaki-Ising model for a classical lattice gas into a quantum model for a superfluid and establish a connection between the normal density fluctuations of the first and the Goldstone mode of the second. The fact that the quantum model we obtain describes a superfluid derives from an inequality by Penrose and Onsager which gives a lower bound to the Bose-Einstein condensate density. Mathematically, the Goldstone mode can be described by means of a “quantum” extension of the local algebra of the Ising model. The classification of its irreducible representations requires an additionalU(1) phase factor and the correspondingU(1) gauge symmetry is spontaneously broken for all finite values of the temperature and of the density.
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  • 72
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    Journal of statistical physics 77 (1994), S. 955-976 
    ISSN: 1572-9613
    Schlagwort(e): Markov property ; Ising model ; critical phenomena ; parallel computational procdures
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract An efficient method of computation for models possessing the Markov property is set out. We apply this method to the two-dimensional ising model and report exact computations for up to 10 by 10 models with periodic boundary conditions. We find that critical-point, finite-size rounding is quite large in the renormalized coupling constant, which is not divergent at the critical point, in contrast to the energy, which is also not divergent and has no rounding there. The difference is traced to the continuity of the energy and the discontinuity of the renormalized coupling constant at the critical point.
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  • 73
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    Journal of statistical physics 78 (1995), S. 147-160 
    ISSN: 1572-9613
    Schlagwort(e): Foam bilayer ; phase transition ; Ising model ; mean-field ; binding energy
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Foam bilayers from individual and mixed phosphatidylcholines are experimentally studied at different temperatures. Occurrence of a chain-melting phase transition in the foam bilayers is detected by two independent parameters—the critical concentrationC c for formation of foam bilayer and the foam bilayer thickness. The data forC c are discussed on the basis of the hole-nucleation theory, which applies the Ising model to foam bilayers and uses the mean-field approximation for interpretation of their stability. This allows the determination of the binding energy of a phospholipid molecule in gel and liquid-crystalline foam bilayers. New possibilities to relate the microscopic and macroscopic characteristics of foam bilayers are demonstrated.
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  • 74
    ISSN: 1572-9613
    Schlagwort(e): Polytypism ; Ising model ; Order-disorder ; X-ray scattering
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Layered crystalline materials like K3Me(CN)6 with Me=Cr, Mn, Fe, Co may often exist in various polytypic forms, due to a variety of choices of layer stacking modes. For cases where the interlayer constellations can be limited to only two energetically almost equivalent ways, the buildup of the crystal may be described by a spin-1/2 Ising-like model. For the system presently being studied one can rationalize the layer stacking to a four-valued choice (i.e., a 1D 4-state Potts case), or use an Ising-like two-sublattice model. Previous diffraction studies of K3Me(CN)6 indicated that two long-range ordered structures prevailed, an orthohombic one named MDO1, with one double layer per repetition unit, and a monoclinic one, MDO2, with two double-layer units. Our studies reveal a more complex situation: The Fe material is for the most part of the MDO2 type. But in addition, in some crystal samples, a hitherto unobserved phase also appears, with six double-layer repetition units, in fact a hybrid of MDO1 and MDO2. The Co material is for the most part of the MDO2 type, but contains in addition a considerable contribution of stacking disorder, as evidenced by the presence of diffuse X-ray scattering lines. The lines do, however, contain distinct maxima, indicating the presence of several layer stacking modes with preference of two, three, four, five, and seven double-layer correlations. The findings can be qualitatively discussed in terms of the ANNNI model.
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  • 75
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    Journal of statistical physics 80 (1995), S. 103-123 
    ISSN: 1572-9613
    Schlagwort(e): Discrete variational problem ; Ising model ; droplets ; metastability
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider a variational problem on thed-dimensional latticeZ d which has applications in the study of the meatastable behavior of the stochastic Ising model. The problem, an isoperimetric one, is to find what is the smallest area a finite subset ofZ d can have restricted to three classes of subsets ofZ d . If ϕ is one of these subsets, we define its volume as the number of points in it and its area as the number of pairs of points inZ d which are neighbors and such that only one of them belongs to ϕ.
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  • 76
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    Journal of statistical physics 86 (1997), S. 1117-1151 
    ISSN: 1572-9613
    Schlagwort(e): Majority rule ; renormalization group ; non-Gibbsianness ; finite-size conditions ; complete analyticity ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We study the majority rule transformation applied to the Gibbs measure for the 2D Ising model at the critical point. The aim is to show that the renormalized Hamiltonian is well defined in the sense that the renormalized measure is Gibbsian. We analyze the validity of Dobrushin-Shlosman uniqueness (DSU) finite-size condition for the “constrained models” corresponding to different configurations of the “image” system. It is known that DSU implies, in our 2D case, complete analyticity from which, as recently shown by Haller and Kennedy. Gibbsianness follows. We introduce a Monte Carlo algorithm to compute an upper bound to Vasserstein distance (appearing in DSU) between finite-volume Gibbs measures with different boundary conditions. We get strong numerical evidence that indeed the DSU condition is verified for a large enough volumeV for all constrained models.
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  • 77
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    Journal of statistical physics 92 (1998), S. 35-45 
    ISSN: 1572-9613
    Schlagwort(e): Competing influences ; Ising model ; Gibbs measures
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We continue a study of Schonmann (1994), Schonmann and Shlosman (1996), and Greenwood and Sun (1997) regarding the competing influences of boundary conditions and external field for the Ising model. We find a critical point B 0 in the competing influences for low temperature in dimension d 2A7E; 2.
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  • 78
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    Journal of statistical physics 92 (1998), S. 785-808 
    ISSN: 1572-9613
    Schlagwort(e): Critical phenomena ; diluted spin systems ; Ising model ; renormalization group
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Within the massive field-theoretic renormalization-group approach the expressions for the β and γ functions of the anisotropic mn-vector model are obtained for general space dimension d in three-loop approximation. Resumming corresponding asymptotic series, critical exponents for the case of the weakly diluted quenched Ising model (m = 1, n = 0), as well as estimates for the marginal order parameter component number m c of the weakly diluted quenched m-vector model, are calculated as functions of d in the region 2 ≤ d 〈 4. Conclusions concerning the effectiveness of different resummation techniques are drawn.
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  • 79
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    Journal of statistical physics 93 (1998), S. 573-582 
    ISSN: 1572-9613
    Schlagwort(e): Scaling ; Ising model ; Markov property ; critical phenomena ; parallel computational procedures
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The idea that near the critical point each block of spins behaves just like a single big spin is investigated. The case where a diamond-shaped block of spins is embedded in a (small) sea of spins is studied. Use is made of the Markov property method to make exact computations of the various spin moments needed to test this hypothesis. The residual fluctuation about the mean value of the block spin is seen to tend to a finite fraction of the length of the mean block-spin. This result is in line with previous studies which used different types of boundary conditions.
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  • 80
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    Journal of statistical physics 97 (1999), S. 87-144 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; anisotropic field ; phase diagram ; cluster expansion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.
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  • 81
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    Journal of statistical physics 98 (2000), S. 551-588 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; universal amplitude ratios ; conformal field theory ; torus ; finite-size scaling ; corrections to scaling ; Monte Carlo ; Swendsen–Wang algorithm ; cluster algorithm
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x ★=lim L→∞ ξ(L)/L and the first four magnetization moment ratios V 2n =〈 $$M$$ 2n 〉/〈 $$M$$ 2〉 n . As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G*2n . We confirm these predictions by a high-precision Monte Carlo simulation.
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  • 82
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    Journal of statistical physics 98 (2000), S. 1063-1073 
    ISSN: 1572-9613
    Schlagwort(e): polygon statistics ; Ising model ; exact solution
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We calculate the number of polygons with fixed total length drawn on a square lattice with periodic boundary conditions. In addition, we study the statistics of polygons with the number of horizontal and vertical links fixed separately. The analysis is performed via a mapping to the Ising model with isotropic and anisotropic interactions. We deal with the case of finite lattice sizes as well as the thermodynamic limit.
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  • 83
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    Journal of statistical physics 64 (1991), S. 251-270 
    ISSN: 1572-9613
    Schlagwort(e): Heisenberg model ; random walk ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We develop random walk representations for the spin-S Heisenberg ferromagnet with nearest neighbor interactions. We show that the spin-S Heisenberg model is a diffusion with local times controlled by the spin-S Ising model. As a consequence, expectations for the Heisenberg model conditioned on zero diffusion are shown to be Ising expectations.
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  • 84
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    Journal of statistical physics 64 (1991), S. 329-361 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; spin glasses ; relaxation phenomena ; random matrices ; multispin coding
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.
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  • 85
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    Journal of statistical physics 58 (1990), S. 355-370 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Potts model ; functional integrals
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A new path integral formulation for theq-state Potts model is proposed. This formulation reproduces known results for the Ising model (q=2) and naturally extends these results for arbitraryq. The mean field results for both the Ising and the Potts models are obtained as a leading saddle point contribution to the corresponding functional integrals, while the systematic computation of corrections to the saddle point contribution produces the Onsager reaction field terms, which forq=2 coincide with results already known for the Ising model.
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  • 86
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    Journal of statistical physics 58 (1990), S. 185-198 
    ISSN: 1572-9613
    Schlagwort(e): Finite ; size analysis ; spectrum calculations ; field theoretical framework ; Ising model ; surface tension
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We measure the surface tensionσ in the broken phase of the 3D Ising model at a temperatureT=0.955T c with two different methods which are taken from quantum field theory in finite volumes. Both methods rely on finite-size effects close to the phase transition. The first one measuresσ from the size dependence of the vacuum tunneling energy, which is determined by the decay of a correlation, givingσ=0.030. The second one extractsσ from the size dependence of the rate of flip events and its corresponding correlation time. It leads toσ=0.027. Both values agree reasonably with other calculations.
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  • 87
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    Journal of statistical physics 58 (1990), S. 467-474 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; border model ; Padé approximants ; series analysis ; universality ; pluralism ; field theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The magnetic susceptibility is studied by the methods of series analysis for the one-dimensional border model (a special case of the continuous-spin Ising model). The structure of this model is analyzed and two conjugate pairs of singularities are found near the real (physical) temperature axis. All the numerical results are consistent with the previously known rigorous results, but do not add to the knowledge of the critical properties.
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  • 88
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    Journal of statistical physics 58 (1990), S. 1127-1135 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; magnetic susceptibility ; exact results
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We explicitly calculate the zero-field magnetic susceptibility of the anisotropic Kagomé lattice Ising model on two different varieties of the parameter space. One of them is the limitH=0 of the solubility condition, obtained in a previous paper by Giacomini, for the model with magnetic field. The other one is the disorder variety of the model, for which a dimensional reduction occurs. These varieties do not contain any nontrivial critical behavior of the model. A functional relation is also established, which relates the zero-field susceptibility for ferromagnetic and competing interactions.
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  • 89
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 61 (1990), S. 1105-1119 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Glauber dynamics ; metastability
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We present a proof of the exponential convergence to equilibrium of single-spin-flip stochastic dynamics for the two-dimensional Ising ferromagnet in the low-temperature case with not too small external magnetic fieldh uniformly in the volume and in the boundary conditions.
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  • 90
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 62 (1991), S. 443-451 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; interfaces ; Monte Carlo simulation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We determine by Monte Carlo simulations the width of an interface between the stable phase and the metastable phase in a two-dimensional Ising model with a magnetic field, in the case of nonconversed order parameter (Glauber dynamics). At zero temperature, the width increases ast β withβ−1/3, as predicted by earlier theories. As temperature increases, the value of the effective exponentβ that we measure decreases toward the value 1/4, which is the value in the absence of magnetic field.
    Materialart: Digitale Medien
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  • 91
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 63 (1991), S. 867-882 
    ISSN: 1572-9613
    Schlagwort(e): Monte Carlo ; statistical errors ; systematic errors ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We have studied the statistical and systematic errors which arise in Monte Carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used. We find that, depending on the degree of self-averaging exhibited by the quantities measured, the statistical errors can increase, decrease, or stay the same as the system size is increased. The systematic underestimation of response functions due to the finite number of measurements made is also studied. We develop a scaling formalism to describe the size dependence of these errors, as well as their dependence on the “bin length” (size of the statistical sample), both at and away from a phase transition. The formalism is tested using simulations of thed=3 Ising model at the infinite-lattice transition temperature. We show that for a 96×96×96 system noticeable systematic errors (systematic underestimation of response functions) are still present for total run lengths of 106 Monte Carlo steps/site (MCS) with measurements taken at regular intervals of 10 MCS.
    Materialart: Digitale Medien
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  • 92
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 63 (1991), S. 1053-1075 
    ISSN: 1572-9613
    Schlagwort(e): Water-oil-surfactant systems ; interfacial composition profiles and tensions ; wetting transition ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The spin-1 Ising model, which is equivalent to the three-component lattice gas model, is used to study wetting transitions in three-component surfactant systems consisting of an oil, water, and a nonionic surfactant. Phase equilibria, interfacial profiles, and interfacial tensions for three-phase equilibrium are determined in mean field approximation, for a wide range of temperature and interaction parameters. Surfactant interaction parameters are found to strongly influence interfacial tensions, reducing them in some cases to ultralow values. Interfacial tensions are used to determine whether the middle phase, rich in surfactant, wets or does not wet the interface between the oil-rich and water-rich phases. By varying temperature and interaction parameters, a wetting transition is located and found to be of the first order. Comparison is made with recent experimental results on wetting transitions in ternary surfactant systems.
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  • 93
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 65 (1991), S. 423-444 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; Bond disorder ; Bethe lattice
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A magnetic model is considered consisting of annealed, mutually repelling ferromagnetic bond impurities in an antiferromagnetic host lattice. Using recurrence relation techniques, the grand-canonical version of this model is solved on the three-coordinated Bethe lattice. A generic phase diagram is obtained containing, apart from the usual ferro- and antiferromagnetic regimes, two distinct incommensurate phases as well as a period-four modulated phase. Evidence is obtained that in one of the two incommensurate phases impurity pairing occurs.
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  • 94
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 65 (1991), S. 1235-1246 
    ISSN: 1572-9613
    Schlagwort(e): Diffusion-annihilation ; Ising model ; kinetics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The relationship between the one-dimensional kinetic Ising model at zero temperature and diffusion-annihilation in one dimension is studied. Explicit asymptotic results for the average domain size, average magnetization squared, and pair-correlation function are derived for the Ising model, for arbitrary initial magnetization. For the case of zero initial magnetization (m 0=0, a number of recent exact results for diffusion-annihilation with random initial conditions are obtained. However, for the casem 0 not equal to zero, the asymptotic behavior turns out to be different from diffusion-annihilation with random initial conditions and at a finite density. In addition, in contrast to the case of diffusion-annihilation, the domain-size distribution scaling functionh(x) is found to depend nontrivially on the initial magnetization. The origin of these differences is clarified and the existence of nontrivial correlations in the initial wall distribution for finite initial magnetization is found to be responsible for these differences. Results of Monte Carlo simulations for the domain size distribution function for different initial magnetizations are also presented.
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  • 95
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 67 (1992), S. 813-818 
    ISSN: 1572-9613
    Schlagwort(e): Dynamic critical exponents ; Glauber and Kawasaki dynamics ; Ising model ; Monte Carlo renormalization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The essential feature of the Kawasaki model is the conserved order parameter, which places the model in class B of the Halperin, Hoheberg, and Ma classification. We have studied the energy relaxation of this model in one and two dimensions with the added feature that spin exchange may take place between any pair of sites within the system. Our results for the dynamic exponentz are indistinguishable from those for class A models, in which the order parameter is not conserved.
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  • 96
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 70 (1993), S. 1121-1148 
    ISSN: 1572-9613
    Schlagwort(e): Stochastic dynamics ; Ising model ; metastability ; crystal growth ; first excursion
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Nucleation from a metastable state is studied for an anisotropic Ising model at very low temperatures. It turns out that the critical nucleus as well as configurations on a typical path to it differ from the Wulff shape of an equilibrium droplet.
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  • 97
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 72 (1993), S. 1-14 
    ISSN: 1572-9613
    Schlagwort(e): Wulff construction ; equilibrium crystal shapes ; Ising model
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We report results about a rigorous microscopic justification of the Wulff construction for the two-dimensional Ising model at low temperatures and under periodic boundary conditions. The idea of the proof is sketched.
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  • 98
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 72 (1993), S. 189-205 
    ISSN: 1572-9613
    Schlagwort(e): Ising model ; dynamic exponents ; power spectra ; Monte Carlo simulations ; dynamics of interface growth ; self-organized criticality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We have simulated the two- and three-dimensional Ising models at their respective critical points with a conventional Monte Carlo algorithm. From the power spectrum of the magnetization autocorrelations we have determined the dynamic critical exponents and obtained the valuesz = 2.16–2.19 andz = 2.05, in agreement with the results quoted in the literature. We have also studied the power spectrum for the Kardar-Parisi-Zhang and Sun-Guo-Grant equations describing interface dynamics. Arguments similar to what was recently used to conclude thatz = 4 -η for model B in critical dynamics were applied to the Sun-Guo-Grant growth model and the known exact values for the roughening and dynamic exponents were obtained. From an analysis of the corresponding power spectrum in self-organized critical sand models one obtains a recently proposed hyperscaling relation.
    Materialart: Digitale Medien
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  • 99
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 72 (1993), S. 417-458 
    ISSN: 1572-9613
    Schlagwort(e): Automata and substitutions ; critical phenomena ; incommensurate structures ; Ising model ; phase transitions ; quantum spin chains ; quasicrystals
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract We consider the quantum spin-1/2 Ising chain in a uniform transverse magnetic field, with an aperiodic sequence of ferromagnetic exchange couplings. This system is a limiting anisotropic case of the classical two-dimensional Ising model with an arbitrary layered modulation. Its formal solution via a Jordan-Wigner transformation enables us to obtain a detailed description of the influence of the aperiodic modulation on the singularity of the ground-state energy at the critical point. The key concept is that of thefluctuation of the sums of any number of consecutive couplings at the critical point. When the fluctuation isbounded, the model belongs to the “Onsager universality class” of the uniform chain. The amplitude of the logarithmic divergence in the specific heat is proportional to the velocity of the fermionic excitations, for which we give explicit expressions in most cases of interest, including the periodic and quasiperiodic cases, the Thue-Morse chain, and the random dimer model. When the couplings exhibit anunbounded fluctuation, the critical singularity is shown to be generically similar to that of the disordered chain: the ground-state energy has finite derivatives of all orders at the critical point, and an exponentially small singular part, for which we give a quantitative estimate. In themarginal case of a logarithmically divergent fluctuation, e.g., for the period-doubling sequence or the circle sequence, there is a negative specific heat exponentα, which varies continuously with the strength of the aperiodic modulation.
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  • 100
    Digitale Medien
    Digitale Medien
    Springer
    Journal of statistical physics 72 (1993), S. 621-641 
    ISSN: 1572-9613
    Schlagwort(e): Monte Carlo ; Markov property ; Ising model ; critical phenomena
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this paper we introduce a new Monte Carlo procedure based on the Markov property. This procedure is particularly well suited to massively parallel computation. We illustrate the method on the critical phenomena of the well known one-dimensional Ising model. In the course of this work we found that the autocorrelation time for the Metropolis Monte Carlo algorithm is closely given by the square of the correlation length. We find speedup factors of the order of 1 million for the method as implemented on the CM2 relative to a serial machine. Our procedure gives error estimates which are quite consistent with the observed deviations from the analytically known exact results.
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