Replica-Exchange Cluster Algorithm

TL;DR

This paper introduces a new flexible Monte Carlo simulation method combining replica-exchange, cluster updates, and adaptive routines, significantly improving efficiency in studying critical phenomena in Ising models.

Contribution

The paper presents a novel combined algorithm that enhances sampling efficiency and extends the temperature/energy range for finite-size scaling analyses.

Findings

Achieved two orders of magnitude performance improvement in 2D and 3D Ising models.

Outperforms Wang-Landau recursion and standard multicanonical methods.

Enables more systematic investigations of critical phenomena.

Abstract

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature/energy range around the critical point. By combining the replica-exchange algorithm with cluster updates and an adaptive routine to find the range of interest, we introduce a new flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain two further orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.