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

摘要

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