A histogram-free multicanonical Monte Carlo algorithm for the basis expansion of density of states

TL;DR

This paper introduces a novel multicanonical Monte Carlo algorithm that directly derives an analytical density of states in a chosen basis, eliminating histogram binning and accelerating convergence in continuous systems.

Contribution

The new algorithm directly computes the density of states as an analytical basis expansion, avoiding histograms and reducing computational steps compared to prior methods.

Findings

Achieves faster convergence with fewer Monte Carlo steps

Provides an analytical form of the density of states

Reduces errors caused by discretization and binning

Abstract

We report a new multicanonical Monte Carlo (MC) algorithm to obtain the density of states (DOS) for physical systems with continuous state variables in statistical mechanics. Our algorithm is able to obtain an analytical form for the DOS 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 (MUCA) sampling and Wang-Landau (WL) sampling. This is enabled by storing the visited states directly in a data set 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.