Reducing quasi-ergodic behavior in Monte Carlo simulations by <i>J</i>-walking: Applications to atomic clusters

TLDR

The paper introduces an easy‑to‑implement method that dramatically reduces quasi‑ergodicity errors in Monte Carlo simulations of systems with large energy barriers. The method couples standard Metropolis sampling to a higher‑temperature Boltzmann distribution via a second random walker, enabling barrier crossing; it is demonstrated on one‑dimensional double wells, higher‑dimensional extensions, and argon Lennard‑Jones clusters. The approach yields remarkable acceleration of convergence for cluster energy and heat capacity near the melting transition, even when starting from random configurations.

Abstract

A method is introduced that is easy to implement and greatly reduces the systematic error resulting from quasi-ergodicity, or incomplete sampling of configuration space, in Monte Carlo simulations of systems containing large potential energy barriers. The method makes possible the jumping over these barriers by coupling the usual Metropolis sampling to the Boltzmann distribution generated by another random walker at a higher temperature. The basic techniques are illustrated on some simple classical systems, beginning for heuristic purposes with a simple one-dimensional double well potential based on a quartic polynomial. The method’s suitability for typical multidimensional Monte Carlo systems is demonstrated by extending the double well potential to several dimensions, and then by applying the method to a multiparticle cluster system consisting of argon atoms bound by pairwise Lennard-Jones potentials. Remarkable improvements are demonstrated in the convergence rate for the cluster configuration energy, and especially for the heat capacity, at temperatures near the cluster melting transition region. Moreover, these improvements can be obtained even in the worst-case scenario where the clusters are initialized from random configurations.