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International Conference on Statistical Physics

作者： Okabe, Y Tomita, Y Yamaguchi, C Tokyo Metropolitan Univ Dept Phys Hachioji Tokyo 1920397 Japan

We explain the idea of the probability-changing cluster (PCC) algorithm, which is an extended version of the Swendsen-Wang algorithm. With this algorithm, we can tune the critical point automatically. We show the effectiveness of the PCC algorithm for the case of the three-dimensional (3D) Ising model. We also apply this new algorithm to the study of the 3D diluted Ising model. Since we tune the critical point of each random sample automatically with the PCC algorithm, we can investigate the sample-dependent critical temperature and the sample average of physical quantities at each critical temperature, systematically. We have also applied another newly proposed algorithm, the Wang-Landau algorithm, to the study of the spin glass problem. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： cluster algorithm Ising model random spin systems

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Critical dynamics of two-replica cluster algorithms

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 2001年第2期12卷 257-271页

作者： Li, XN Machta, J Univ Massachusetts Dept Phys Amherst MA 01003 USA

The dynamic critical behavior of the two-replica cluster algorithm is studied. Several versions of the algorithm are applied to the two-dimensional, square lattice Ising model with a staggered field. The dynamic exponent for the full algorithm is found to be less than 0.4. It is found that odd translations of one replica with respect to the other together with global flips are essential for obtaining a small value of the dynamic exponent.

关键词： cluster algorithm ising antiferromagnet critical dynamics

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A Monte Carlo test of the Fisher-Nakanishi-Scaling theory for the capillary condensation critical point

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JOURNAL OF CHEMICAL PHYSICS 2001年第13期114卷 5853-5862页

作者： Dillmann, O Janke, W Müller, M Binder, K Univ Mainz Inst Phys D-55099 Mainz Germany Inst Theoret Phys D-04109 Leipzig Germany

Extending the Swendsen-Wang cluster algorithm to include both bulk (H) and surface fields (H-1) in LxLxD Ising films of thickness D and two free LxL surfaces, a Monte Carlo study of the capillary condensation critical point of the model is presented. Applying a finite-size scaling analysis where the lateral linear dimension L is varied over a wide range, the critical temperature T-c(D) and the associated critical field H-c(D) are estimated for 4 less than or equal toD less than or equal to 32 lattice spacings, for a choice of the surface field H-1 small enough that the dependence of H-c(D) on H-1 is still linear. It is shown that the results are consistent with the power laws predicted by Fisher and Nakanishi [M. E. Fisher and H. Nakanishi, J. Chem. Phys. 75, 5857 (1981)], namely T-c(infinity)-T-c(D)proportional toD(-1/nu), H-c(D)proportional toD(-(Delta-Delta1)/nu), where nu is the bulk correlation length exponent of the three-dimensional Ising model, and Delta, Delta (1) are the corresponding "gap exponents" associated with bulk and surface fields, respectively. As expected, the order parameter of the thin film near its critical point exhibits critical behavior compatible with the universality class of the two-dimensional Ising model. (C) 2001 American Institute of Physics.

关键词： .THREE-DIMENSIONAL exponent critical temperature Critical Behavior capillary nite-size thin film bulk and surface Chem Phys cluster algorithm Ising films lateral linear

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Meron-cluster algorithms and chiral-symmetry breaking in a (2+1)D staggered fermion model

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NUCLEAR PHYSICS B 2000年第1-2期583卷 331-346页

作者： Cox, J Holland, K MIT Ctr Theoret Phys Nucl Sci Lab Dept Phys Cambridge MA 02139 USA Univ Bern Inst Theoret Phys CH-3012 Bern Switzerland

The recently developed meron-cluster algorithm completely solves the exponentially difficult sign problem for a number of models previously inaccessible to numerical simulation. We use this algorithm in a high-precision study of a model of N = 1 flavor of staggered fermions in (2 + 1) dimensions with a four-fermion interaction. This model cannot be explored using standard algorithms. We find that the 2(2) chiral symmetry of this model is spontaneously broken at low temperatures and that the finite-temperature chiral phase transition is in the universality class of the 2D Ising model, as expected. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： chiral symmetry symmetry breaking fermion algorithm cluster algorithm meron Monte Carlo

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Universal amplitude ratios in the critical two-dimensional Ising model on a torus

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JOURNAL OF STATISTICAL PHYSICS 2000年第3-4期98卷 551-588页

作者： Salas, J Sokal, AD Univ Zaragoza Fac Ciencias Dept Fis Teor Zaragoza 50009 Spain Univ Zaragoza Fac Ciencias Dept Fis Mat Condensada Zaragoza 50009 Spain NYU Dept Phys New York NY 10003 USA

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-->infinity) xi(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.

关键词： Ising model universal amplitude ratios conformal field theory torus finite-size scaling corrections to scaling Monte Carlo Swendsen-Wang algorithm cluster algorithm

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cluster Monte Carlo study of multicomponent fluids of the Stillinger-Helfand and Widom-Rowlinson type

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Physical Review E 2000年第2期62卷 2226-2226页

作者： Rongfeng Sun Harvey Gould J. Machta L. W. Chayes Department of Mathematics University of California Los Angeles California 90095-1555

Phase transitions of fluid mixtures of the type introduced by Stillinger and Helfand are studied using a continuum version of the invaded cluster algorithm. Particles of the same species do not interact, but particles of different types interact with each other via a repulsive potential. Examples of interactions include the Gaussian molecule potential and a repulsive step potential. Accurate values of the critical density, fugacity, and magnetic exponent are found in two and three dimensions for the two-species model. The effect of varying the number of species and of introducing quenched impurities is also investigated. In all the cases studied, mixtures of q species are found to have properties similar to q-state Potts models.

关键词： .quenched repulsive interact fugacity critical density Potts models invaded WIDOM-ROWLINSON cluster Monte Carlo cluster algorithm same species molecule potential

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cluster algorithms for spatial point processes with symmetric and shift invariant interactions

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 1999年第2期8卷 353-372页

作者： Cai, HY Univ Missouri Dept Math & Comp Sci St Louis MO 63121 USA

In this article, Swendsen-Wang-Wolff algorithms are extended to simulate spatial point processes with symmetric and stationary interactions. Convergence of these algorithms is considered. Some further generalizations of the algorithms are discussed. The ideas presented in this article can also be useful in handling some large and complicated systems.

关键词： cluster algorithm convergence of Markov chain Monte Carlo simulation spatial point process

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cluster methods for Ising systems with fields

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 1999年第8期10卷 1427-1432页

作者： Machta, J Univ Massachusetts Dept Phys & Astron Amherst MA 01002 USA

Efficient cluster algorithms for Ising systems with fields are described. cluster are grown between two replicas of the system in the same field. As is the case for other successful cluster approaches, the critical po... 详细信息

关键词： Ising model cluster algorithm replica exchange model

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Antiferromagnetic potts models on the square lattice: A high-precision Monte Carlo study

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JOURNAL OF STATISTICAL PHYSICS 1999年第3-4期96卷 461-530页

作者： Ferreira, SJ Sokal, AD Univ Fed Minas Gerais Dept Estatist ICEx BR-30161970 Belo Horizonte MG Brazil NYU Dept Phys New York NY 10003 USA

study the antiferromagnetic q-state Potts model on the square lattice for q = 3 and q = 4, using the Wang-Swendsen-Kotecky (WSK) Monte Carlo algorithm and a powerful finite-size-scaling extrapolation method. For q=3 we obtain good control up to correlation length xi similar to 5000;the data are consistent with xi(B)=Ae(2 beta)beta(P)(1 + a(1)e(-beta) + ...) as beta--> infinity, with p approximate to 1. The staggered susceptibility behaves as chi(stagg) similar to xi(5/3). For q = 4 the model is disordered (xi less than or similar to 2) even at zero temperature. In appendices we prove a correlation inequality for Potts antiferromagnets on a bipartite lattice, and we prove ergodicity of the WSK algorithm at zero temperature for Potts antiferromagnets on a bipartite lattice.

关键词： Potts model antiferromagnet square lattice phase transition zero-temperature critical point Monte Carlo cluster algorithm Swendsen-Wang algorithm Wang-Swendsen-Kotecky algorithm finite-size scaling

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Study of phase separation in a first-order phase transition:: Nucleation versus spinodal decomposition

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 1999年第7期10卷 1261-1269页

作者： Arkin, H Çelik, T Berg, BA Meyer-Ortmanns, H Hacettepe Univ Dept Phys Ankara Turkey Florida State Univ Dept Phys Tallahassee FL 32306 USA Univ Gesamthsch Wuppertal Fachbereich Phys Wuppertal Germany

Studies of dynamical properties of first-order phase transition for a scalar field theory indicate that the phase conversion mechanism itself depends on the strength of the first-order transition: if the transition is strongly (weakly) first-order, bubble nucleation (spinodal decomposition) are favored conversion mechanisms, respectively. These distinct scenarios are of phenomenological impact. In order to see which phase conversion mechanism takes place depending on the strength of transition, we have simulated the q = 5 state Potts model in two dimensions with an external magnetic field. The transition gets weakened in its first-order as the external field increases. Our results indicate that the phase conversion mechanism changes from nucleation to spinodal decomposition.

关键词： phase separation Potts model spinodal decomposition cluster algorithm bubble nucleation deconfinement transition

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