An improved Monte Carlo method for direct calculation of the density of states

TL;DR

This paper introduces an improved Monte Carlo algorithm that efficiently estimates the density of states by leveraging transition probabilities, enhancing sampling uniformity and accuracy in both lattice and continuum systems.

Contribution

The paper presents a novel Monte Carlo method combining transition probability statistics with Wang-Landau sampling for better density of states estimation.

Findings

Effective in Lennard-Jones liquid simulations

Achieves rapid convergence and uniform sampling

Applicable to both lattice and continuum models

Abstract

We present an efficient Monte Carlo algorithm for determining the density of states which is based on the statistics of transition probabilities between states. By measuring the infinite temperature transition probabilities--that is, the probabilities associated with move proposal only--we are able to extract excellent estimates of the density of states. When this estimator is used in conjunction with a Wang-Landau sampling scheme [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling of macrostates (e.g., energies) and systematically refine the calculated density of states. This approach requires only potential energy evaluations, continues to improve the statistical quality of its results as the simulation time is extended, and is applicable to both lattice and continuum systems. We test the algorithm on the Lennard-Jones liquid and demonstrate good statistical convergence properties.