Cluster Monte Carlo algorithms

TL;DR

This paper reviews cluster Monte Carlo algorithms, focusing on their application to various physical systems like spin models and hard spheres, highlighting recent developments and the pivot cluster method.

Contribution

It offers a comprehensive overview of cluster algorithms, emphasizing recent applications and the pivot cluster method for entropic systems.

Findings

Enhanced understanding of cluster algorithms in statistical physics

Application of pivot cluster method to hard spheres

Recent advancements in cluster Monte Carlo techniques

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.