Cluster dynamics for first-order phase transitions in the Potts model

TL;DR

This paper introduces a novel Monte Carlo algorithm that dynamically adjusts transition parameters and employs cluster steps to efficiently simulate first-order phase transitions in the Potts model, overcoming tunneling suppression.

Contribution

The paper presents a new algorithm that makes transition parameters dynamic and uses cluster steps, improving simulation efficiency for first-order phase transitions.

Findings

Demonstrates improved tunneling between phases

Shows efficiency gains in Potts model simulations

Validates method with numerical results

Abstract

An algorithm for Monte Carlo simulations is proposed in which the parameter controlling the strength of the transition becomes a dynamical variable and in which efficient transitions are achieved by cluster steps. It allows to avoid the strongly suppressed tunneling between the phases by travelling easily via the second order region. Numerical results for the Potts model are presented which demonstrate the advantages of the method.