Replica Monte Carlo Simulation (Revisited)

TL;DR

This paper revisits the replica Monte Carlo algorithm for spin glasses, comparing it with replica exchange and Houdayer's cluster algorithm, and presents new results on correlation times in 2D and 3D.

Contribution

It provides a comprehensive review of the original replica Monte Carlo algorithm and introduces new findings on its correlation times compared to other methods.

Findings

Replica Monte Carlo's correlation times are analyzed in 2D and 3D.

Comparison shows differences between replica Monte Carlo and replica exchange.

The paper discusses the relationship between various cluster algorithms.

Abstract

In 1986, Swendsen and Wang proposed a replica Monte Carlo algorithm for spin glasses [Phys. Rev. Lett. 57 (1986) 2607]. Two important ingredients are present, (1) the use of a collection of systems (replicas) at different of temperatures, but with the same random couplings, (2) defining and flipping clusters. Exchange of information between the systems is facilitated by fixing the tau spin (tau=sigma^1\sigma^2) and flipping the two neighboring systems simultaneously. In this talk, we discuss this algorithm and its relationship to replica exchange (also known as parallel tempering) and Houdayer's cluster algorithm for spin glasses. We review some of the early results obtained using this algorithm. We also present new results for the correlation times of replica Monte Carlo dynamics in two and three dimensions and compare them with replica exchange.