Multicanonical Methods vs. Molecular Dynamics vs. Monte Carlo: Comparison for Lennard-Jones Glasses

TL;DR

This study compares multicanonical algorithms, Monte Carlo, and molecular dynamics in finding low-energy states of Lennard-Jones glasses, revealing limited advantages of entropic sampling for larger systems due to entropy barriers.

Contribution

The paper demonstrates that multicanonical methods offer minimal benefits over traditional techniques in large Lennard-Jones systems, highlighting their limitations in overcoming entropy barriers.

Findings

Multicanonical methods show slight benefits in small systems (<80 particles).

Benefits of multicanonical methods disappear as system size increases.

Multicanonical methods become similar to simulated annealing in the thermodynamic limit.

Abstract

We applied a multicanonical algorithm (entropic sampling) to a two-dimensional and a three-dimensional Lennard-Jones system with quasicrystalline and glassy ground states. Focusing on the ability of the algorithm to locate low lying energy states, we compared the results of the multicanonical simulations with standard Monte Carlo simulated annealing and molecular dynamics methods. We find slight benefits to using entropic sampling in small systems (less than 80 particles), which disappear with larger systems. This is disappointing as the multicanonical methods are designed to surmount energy barriers to relaxation. We analyze this failure theoretically, and show (1) the multicanonical method is reduced in the thermodynamic limit (large systems) to an effective Monte Carlo simulated annealing with a random temperature vs. time, and (2) the multicanonical method gets trapped by unphysical entropy barriers in the same metastable states whose energy barriers trap the traditional quenches. The performance of Monte Carlo and molecular dynamics quenches were remarkably similar.