Cluster Monte Carlo algorithms

Abstract

In recent years, a better understanding of the Monte Carlo method has provided us with many new techniques in different areas of statistical physics. Of particular interest are so called cluster methods, which exploit the considerable algorithmic freedom given by the detailed balance condition. Cluster algorithms appear, among other systems, in classical spin models, such as the Ising model, in lattice quantum models (bosons, quantum spins and related systems) and in hard spheres and other `entropic' systems for which the configurational energy is either zero or infinite. In this chapter, we discuss the basic idea of cluster algorithms with special emphasis on the pivot cluster method for hard spheres and related systems, for which several recent applications are presented.We provide less technical detail but more context than in the original papers.