Histogram-free multicanonical Monte Carlo sampling to calculate the density of states

Abstract

We report a new multicanonical Monte Carlo algorithm to obtain the density of states for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain a closed-form expression for the density of states expressed in a chosen basis set, instead of a numerical array of finite resolution as in previous variants of this class of MC methods such as the multicanonical sampling and Wang–Landau sampling. This is enabled by storing the visited states directly and avoiding the explicit collection of a histogram. This practice also has the advantage of avoiding undesirable artificial errors caused by the discretization and binning of continuous state variables. Our results show that this scheme is capable of obtaining converged results with a much reduced number of Monte Carlo steps, leading to a significant speedup over existing algorithms. Program summaryProgram Title: HistogramFreeMUCAProgram Files doi:http://dx.doi.org/10.17632/mtgyvsfzyg.1Licensing provisions: BSD 3-clauseProgramming language: PythonNature of problem: This program implements a novel algorithm to obtain the density of states of a physical system, expanded in a chosen basis set. Unlike existing algorithms that return the density of states as a numerical array, this algorithm avoids binning of a continuous variable and is able to express the density of states as a closed-form expression. It is thus suitable for the study of the statistical mechanics and thermodynamic properties of physical systems where the density of a continuous state variable is of interest.Solution method: The new algorithm presented here is a special reweighting method in classical Monte Carlo approaches. In particular, it can be regarded as a descendant and a hybrid method closely related to the multicanonical method and Wang–Landau sampling.Additional comments: Most updated source code can be found at: https://github.com/yingwaili/HistogramFreeMUCA