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中国科学通报：英文版

Monte Carlo simulations for two-dimensional Ising system far from equilibrium

Lei Lei, Xiaowei Xiaowei, Zheng, Ji, Zhao, Xiaoyu

Published Jan 1, 2007• 0 citations
OpenAlex

Abstract

与动态蒙特卡罗模拟，它没有批评慢下来，以非平衡状态的二维的 Ising 模型的批评行为被调查。我们集中于二时间的自相关功能 A (t， t') 在二个不同进化阶段识别动态代表 z，分别地在 T_c 从一个高温度状态和一个完全订的状态熄灭了到临界态。由使用 heat-bathalgorithm，动态批评代表作为 z ≈被估计 2.16。作为结果，可伸缩的行为的普遍性数字地被验证，并且代表λ _ c 是坚定的由λ _ c = 完全为来自一个起始的完全订的状态的进化的β / v。

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与动态蒙特卡罗模拟，它没有批评慢下来，以非平衡状态的二维的 Ising 模型的批评行为被调查。我们集中于二时间的自相关功能 A (t， t') 在二个不同进化阶段识别动态代表 z，分别地在 T_c 从一个高温度状态和一个完全订的状态熄灭了到临界态。由使用 heat-bathalgorithm，动态批评代表作为 z ≈被估计 2.16。作为结果，可伸缩的行为的普遍性数字地被验证，并且代表λ _ c 是坚定的由λ _ c = 完全为来自一个起始的完全订的状态的进化的β / v。
Monte Carlo simulations are performed on the square lattice Ising system with both the nearest neighbor and the two-dimensional dipolar interactions in order to investigate the critical property of ferromagnetic phase transitions in this 2-dimensional system. Applying the finite size scaling theory to Monte Carlo data just near the transition point, the critical indices of this dipolar system are calculated and α=0.31±0.04, β =0.20±0.02, γ=1.08±0.20 and ν=0.72±0.10 are obtained. However, in the temperature region considerably far from the transition point, different values of α, β and γ seem to be adequate, which are rather close to those of the rigorous result of the 2-dimensional Ising model.
The four-dimensional Ising model is simulated on Creutz cellular automatons using finite lattices with linear dimensions 4 ≤ L ≤ 8. The temperature variations and finite-size scaling plots of the specific heat and the Binder parameter verify the theoretically predicted expression near the infinite lattice critical temperature for 7, 14, and 21 independent simulations. Approximate values for the critical temperature of the infinite lattice of Tc(∞) = 6.6965(35), 6.6961(30), 6.6960(12), 6.6800(3), 6.6801(2), 6.6802(1) and 6.6925(22) (without the logarithmic factor), 6.6921(22) (without the logarithmic factor), 6.6909(2) (without the logarithmic factor), 6.6822(13) (with the logarithmic factor), 6.6819(11) (with the logarithmic factor), and 6.6808(8) (with the logarithmic factor) are obtained from the intersection points of the specific heat curves, the Binder parameter curves, and straight line fits of specific heat maxima for 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the results, 6.6802(1) and 6.6808(8), are in very good agreement with the results of a series expansion of Tc(∞), 6.6817(15) and 6.6802(2), the dynamic Monte Carlo value Tc(∞) = 6.6803(1), the cluster Monte Carlo value Tc(∞) = 6.680(1), and the Monte Carlo value using the Metropolis-Wolff cluster algorithm Tc(∞) = 6.6802632 ± 5 · 10−5. The average values calculated for the critical exponent of the specific heat are α =− 0.0402(15), − 0.0393(12), − 0.0391(11) with 7, 14, and 21 independent simulations, respectively. As the number of independent simulations increases, the result, α =− 0.0391(11), agrees with the series expansions result, α =− 0.12 ± 0.03 and the Monte Carlo result using the Metropolis-Wolff cluster algorithm, α ≥ 0 ± 0.04. However, α =− 0.0391(11) is inconsistent with the renormalization group prediction of α = 0.
We present Monte Carlo simulation results for the dynamical critical exponent z of the two- and three-dimensional kinetic Ising model. The z-values were calculated from the magnetization relaxation from an ordered state into the equilibrium state at Tc for very large systems with up to (169984)2 and (3072)3 spins. To our knowledge, these are the largest Ising-systems simulated todate. We also report the successful simulation of very large lattices on a massively parallel MIMD computer with high speedups of approximately 1000 and an efficiency of about 0.93.