Efficient simulation of the random-cluster model

TL;DR

This paper presents an efficient implementation of Sweeny's algorithm for the random-cluster model, significantly reducing critical slowing down in simulations near phase transitions by leveraging recent advances in dynamic connectivity algorithms.

Contribution

The paper introduces a novel, efficient implementation of Sweeny's cluster algorithm for the random-cluster model, improving simulation performance near critical points.

Findings

Enhanced simulation efficiency near critical points

Reduction in critical slowing down compared to previous algorithms

Successful application of dynamic connectivity algorithms

Abstract

The simulation of spin models close to critical points of continuous phase transitions is heavily impeded by the occurrence of critical slowing down. A number of cluster algorithms, usually based on the Fortuin-Kasteleyn representation of the Potts model, and suitable generalizations for continuous-spin models have been used to increase simulation efficiency. The first algorithm making use of this representation, suggested by Sweeny in 1983, has not found widespread adoption due to problems in its implementation. However, it has been recently shown that it is indeed more efficient in reducing critical slowing down than the more well-known algorithm due to Swendsen and Wang. Here, we present an efficient implementation of Sweeny's approach for the random-cluster model using recent algorithmic advances in dynamic connectivity algorithms.