Cluster Monte Carlo algorithms and their applications

Abstract

We introduce the Markov chain Monte Carlo method and review the background of the cluster algorithms in statistical physics. One of the first such successful algorithm was developed by Swendsen and Wang eight years ago. In contrast to the local algorithms, cluster algorithms update dynamical variables in a global fashion. Therefore, large changes are made in a single step. The method is very efficient, especially near the critical point of a second-order phase transition. Studies of various statistical mechanics models and some generalizations of the algorithm will be briefly reviewed. We mention applications in other fields, especially in imaging processing.