Monte Carlo simulations of glass-forming liquids beyond Metropolis

TL;DR

This paper explores advanced Monte Carlo algorithms for simulating glass-forming liquids, demonstrating that collective moves significantly improve sampling efficiency over standard methods in complex energy landscapes.

Contribution

The study introduces and compares new Monte Carlo algorithms with collective moves, showing enhanced efficiency in sampling rugged free energy landscapes of glassy systems.

Findings

Collective moves outperform local Metropolis in sampling efficiency.

Breaking detailed balance further improves Monte Carlo sampling.

Monte Carlo remains a versatile tool for low-temperature supercooled liquids.

Abstract

Monte Carlo simulations are widely employed to measure the physical properties of glass-forming liquids in thermal equilibrium. Combined with local Monte Carlo moves, the Metropolis algorithm can also be used to simulate the relaxation dynamics, thus offering an efficient alternative to molecular dynamics. Monte Carlo simulations are however more versatile, because carefully designed Monte Carlo algorithms can more efficiently sample the rugged free energy landscape characteristic of glassy systems. After a brief overview of Monte Carlo studies of glass-formers, we define and implement a series of Monte Carlo algorithms in a three-dimensional model of polydisperse hard spheres. We show that the standard local Metropolis algorithm is the slowest, and that implementing collective moves or breaking detailed balance enhances the efficiency of the Monte Carlo sampling. We use time correlation functions to provide a microscopic interpretation of these observations. Seventy years after its invention, the Monte Carlo method remains the most efficient and versatile tool to compute low-temperatures properties in supercooled liquids.