• 大学生园地 •

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

1. 北京师范大学 物理学系，北京 100875
• 收稿日期:2021-03-05 修回日期:2021-06-03 出版日期:2022-01-20 发布日期:2022-01-14
• 作者简介:徐 琳( 2001—) ，女，吉林白城人，北京师范大学物理学系 2018 级本科生.

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

XU Lin，CHEN Yu-ze，LIU Jia-hao

1.  Department of Physics，Beijing Normal University，Beijing 100875，China
• Received:2021-03-05 Revised:2021-06-03 Online:2022-01-20 Published:2022-01-14

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.

Abstract:

Ising model is a widely used magnetic spin interaction model. It is very complicated to

solve the ana- lytic 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 in- troductions of Monte Carlo algorithm in undergraduate courses. In this paper，we use

these three algorithms to simu- late 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.