New Monte Carlo algorithms for classical spin systems

TL;DR

This paper reviews recent cluster-flipping Monte Carlo algorithms designed for efficient simulation of classical spin systems near criticality, including their application to various models like Ising and Potts.

Contribution

It provides a comprehensive overview of new cluster algorithms and their application to different classical spin models, highlighting advancements in simulation efficiency.

Findings

Enhanced simulation efficiency near critical points

Application to Ising, Potts, and continuous spin models

Comparison of various cluster algorithms

Abstract

We describe a number of recently developed cluster-flipping algorithms for the efficient simulation of classical spin models near their critical temperature. These include the algorithms of Wolff, Swendsen and Wang, and Niedermeyer, as well as the limited cluster algorithm, the multigrid methods of Kandel and co-workers, and the invaded cluster algorithm. We describe the application of these algorithms to Ising, Potts, and continuous spin models. This paper is a review to appear in "Monte Carlo Methods in Chemical Physics", D. Ferguson, J. I. Siepmann, and D. G. Truhlar (eds.), Wiley, New York (1997).