Efficient implementation of the Wang-Landau algorithm for systems with length-scalable potential energy functions

TL;DR

This paper introduces an efficient way to implement the Wang-Landau algorithm for systems with length-scalable potentials, enabling better evaluation of thermodynamic properties in such systems.

Contribution

The authors develop a scaled-box Wang-Landau method focusing on potential energy, applicable to systems with length-scalable interactions, demonstrated on binary star and harmonic trap models.

Findings

Efficient Wang-Landau implementation for scalable potential systems.

Accurate density of states evaluation in scaled and physical systems.

Validation on binary star and ideal gas models.

Abstract

We consider a class of systems where $N$ identical particles with positions ${\bf q}_1,...,{\bf q}_N$ and momenta ${\bf p}_1,...,{\bf p}_N$ are enclosed in a box of size $L$, and exhibit the scaling $\mathcal{U}(L{\bf r}_1,...,L{\bf r}_N)=\alpha(L)\, \mathcal{U}({\bf r}_1,...,{\bf r}_N)$ for the associated potential energy function $\mathcal{U}({\bf q}_1,...,{\bf q}_N)$. For these systems, we propose an efficient implementation of the Wang-Landau algorithm for evaluating thermodynamic observables involving energy and volume fluctuations in the microcanonical description, and temperature and volume fluctuations in the canonical description. This requires performing the Wang-Landau simulation in a scaled box of unit size and evaluating the density of states corresponding to the potential energy part only. To demonstrate the efficacy of our approach, as example systems, we consider Padmanabhan's binary star model and an ideal gas trapped in a harmonic potential within the box.