On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble

TL;DR

This paper rigorously derives an off-lattice implementation of the Wang-Landau algorithm for atomic systems, enabling accurate sampling of the configurational space and thermodynamic properties in continuum simulations.

Contribution

It introduces a rigorous framework for off-lattice Wang-Landau sampling using a 'uniform' ensemble, extending the method to continuum atomic systems.

Findings

Good agreement with literature for Lennard-Jones vapor-liquid coexistence

Two implementation variants successfully demonstrated

Framework enables correct thermodynamic calculations in continuum systems

Abstract

We present a rigorous derivation for off-lattice implementations of the so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte-Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a "uniform" ensemble for configurational degrees of freedom--in which all potential energies, volumes, and numbers of particles are equally probable--we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.