Multicanonical methods, molecular dynamics, and Monte Carlo methods: Comparison for Lennard-Jones glasses

We applied a multicanonical algorithm 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 multicanonical 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 that (i) 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 (ii) 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.