Monte-Carlo法模拟二维Ising模型——Metropolis、Swendsen-Wang与Wolff算法的对比  

Monte-Carlo simulation of 2-D Ising model——application of Metropolis,Swendsen-Wang and Wolff algorithm

作　　者：徐琳 陈雨泽 刘家昊 XU Lin;CHEN Yu-ze;LIU Jia-hao(Department of Physics,Beijing Normal University,Beijing 100875,China)

机构地区：[1]北京师范大学物理学系,北京100875

出　　处：《大学物理》2022年第1期79-83,共5页College Physics

摘　　要：Ising模型是一种应用广泛的磁自旋相互作用模型,其二维情况严格求解极为复杂,实际应用中通常利用Wolff算法进行模拟.Wolff算法目前被认为是最好的聚类翻转Monte-Carlo算法.Metropolis和Swendsen-Wang算法同Wolff算法类似,理论上也适用于Ising模型的模拟,却未有文章将三者系统对比来说明Wolff算法的优越性,本科课程对于Monte-Carlo算法的介绍也较少.本文分别利用三种算法模拟了二维Ising模型,介绍了其算法原理、参数选择及实现方式,分析对比了三种算法的模拟效果和适用范围,从而总结说明在二维Ising模型的模拟中Wolff算法效果更好的原因.Ising model is a widely used magnetic spin interaction model.It is very complicated to solve the analytic solution in 2-D case.In practical application,Wolff algorithm is usually used to simulate the Ising model and it is considered to be the best clustering flipping Monte Carlo algorithm.Metropolis and Swendsen-Wang algorithms are similar to Wolff algorithm,and theoretically they are also applicable to the simulation of Ising model.So far,there is no paper has compared the three algorithms to show the advantages of Wolff algorithm,and there are few introductions of Monte Carlo algorithm in undergraduate courses.In this paper,we use these three algorithms to simulate 2-D Ising model and introduce the principle,parameter selection and implementation of the algorithms.In the end,we compare the simulation effect and application range of the three algorithms,and summarize the reason why Wolff algorithm has better effect in the simulation of 2D Ising model.

关 键 词：二维ISING模型 MONTE-CARLO法 Metropolis算法 Wolff算法 Swendsen-Wang算法 

分 类 号：O411.3[理学—理论物理]