Parallel-tempering cluster algorithm for computer simulations of critical phenomena

TL;DR

This paper introduces a combined parallel tempering and cluster update algorithm with an adaptive routine, significantly improving the efficiency of Monte Carlo simulations for studying critical phenomena in 2D and 3D Ising models.

Contribution

It presents a novel, flexible method that enhances finite-size scaling analyses by integrating parallel tempering, cluster updates, and adaptive temperature window selection.

Findings

Achieves 10-100x performance improvement over previous methods

Effective for 2D and 3D Ising models near critical points

Outperforms Wang-Landau recursion in efficiency

Abstract

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two 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.