关键词: 二维 Ising 模型, Monte-Carlo 法, Metropolis 算法, Wolff 算法, Swendsen-Wang 算法

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.

Key words: 2 - D Ising model, Monte - Carlo algorithm, Metropolis algorithm, Wolff algorithm, Swendsen - Wang algorithm