A New Monte Carlo Method and Its Implications for Generalized Cluster Algorithms

Abstract

We describe a novel switching algorithm based on a ``reverse'' Monte Carlo method, in which the potential is stochastically modified before the system configuration is moved. This new algorithm facilitates a generalized formulation of cluster-type Monte Carlo methods, and the generalization makes it possible to derive cluster algorithms for systems with both discrete and continuous degrees of freedom. The roughening transition in the sine-Gordon model has been studied with this method, and high-accuracy simulations for system sizes up to $1024^2$ were carried out to examine the logarithmic divergence of the surface roughness above the transition temperature, revealing clear evidence for universal scaling of the Kosterlitz-Thouless type.