Efficient simulation of the random-cluster model

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.

RevTeX 4.1, 14 pages, 8 figures, 3 tables, version as published

References in corpus (5)

• Critical speeding-up in a local dynamics for the random-cluster model
• Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm
• Generalized-ensemble simulations and cluster algorithms
• Conformal Curves in Potts Model: Numerical Calculation
• Duality of critical interfaces in Potts model: numerical check

Cited by in corpus (13)

• Cluster Monte Carlo and dynamical scaling for long-range interactions
• Corner contribution to cluster numbers in the Potts model
• Fragmentation of fractal random structures
• Solution of the sign problem in the Potts model at fixed fermion number
• Active spanning trees and Schramm-Loewner evolution
• Bridges in the random-cluster model
• Percolation of the Site Random-Cluster Model by Monte Carlo Method
• Dynamic connectivity algorithms for Monte Carlo simulations of the random-cluster model
• On the coupling time of the heat-bath process for the Fortuin-Kasteleyn random-cluster model
• Sweeny dynamics for the random-cluster model with small $Q$
• Universality of the complete-graph Potts model with $0<q\le 2$
• Comparison of the clock, stochastic cutoff, and Tomita Monte Carlo methods in simulating the dipolar triangular lattice at criticality
• Critical points of the random cluster model with Newman-Ziff sampling