A Rapid Dynamical Monte Carlo Algorithm for Glassy Systems

TL;DR

This paper introduces a new dynamical Monte Carlo algorithm tailored for glassy systems, significantly enhancing computational efficiency by exploiting clustering conditions and trapping in deep local minima.

Contribution

The paper presents a novel dynamical Monte Carlo algorithm that improves speed by several orders of magnitude for glassy systems compared to existing methods.

Findings

Achieved several orders of magnitude speedup in simulations.

Validated the algorithm on the Bernasconi model.

Demonstrated effectiveness in systems with deep local minima.

Abstract

In this paper we present a dynamical Monte Carlo algorithm which is applicable to systems satisfying a clustering condition: during the dynamical evolution the system is mostly trapped in deep local minima (as happens in glasses, pinning problems etc.). We compare the algorithm to the usual Monte Carlo algorithm, using as an example the Bernasconi model. In this model, a straightforward implementation of the algorithm gives an improvement of several orders of magnitude in computational speed with respect to a recent, already very efficient, implementation of the algorithm of Bortz, Kalos and Lebowitz.