Novel Monte Carlo algorithms and their applications

TL;DR

This paper introduces a generalized probability-changing cluster algorithm, applies it to the 2D 6-state clock model, and combines it with extended ensemble methods, providing new Monte Carlo techniques for statistical physics models.

Contribution

It presents a novel generalized PCC algorithm based on finite-size scaling of the correlation ratio and combines it with extended ensemble methods, expanding Monte Carlo simulation tools.

Findings

Effective generalized PCC algorithm for 2D clock model

Rigorous broad histogram relation for bond number

New Monte Carlo dynamics for 3D Ising and Potts models

Abstract

We describe a generalized scheme for the probability-changing cluster (PCC) algorithm, based on the study of the finite-size scaling property of the correlation ratio, the ratio of the correlation functions with different distances. We apply this generalized PCC algorithm to the two-dimensional 6-state clock model. We also discuss the combination of the cluster algorithm and the extended ensemble method. We derive a rigorous broad histogram relation for the bond number. A Monte Carlo dynamics based on the number of potential moves for the bond number is proposed, and applied to the three-dimensional Ising and 3-state Potts models.