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 effe...
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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.
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 expon...
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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.
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...
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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.
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-precisi...
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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.
作者:
Salas, JSokal, ADUniv 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--...
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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.
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...
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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.
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 ...
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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.
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...
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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 point of the spin system coincides with the percolation threshold of the clusters. Applications are discussed.
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 w...
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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.
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...
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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.
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