Estimation of critical behavior from the density of states in Classical Statistical Models

TL;DR

This paper introduces a simple approximation method based on the density of states to efficiently estimate critical behavior in large classical statistical models, improving accuracy and scalability of simulations.

Contribution

It presents a novel algorithmic approach that predicts the critical energy space, enabling larger system simulations and accurate critical parameter estimation.

Findings

Accurately predicts the critical part of energy space for large systems.

Successfully applied to Ising models on square and cubic lattices.

Verifies the scaling law relating critical energy space to the thermal critical exponent.

Abstract

We present a simple and efficient approximation scheme which greatly facilitates extension of Wang-Landau sampling (or similar techniques) in large systems for the estimation of critical behavior. The method, presented in an algorithmic approach, is based on a very simple idea, familiar in statistical mechanics from the notion of thermodynamic equivalence of ensembles and the central limit theorem. It is illustrated that, we can predict with high accuracy the critical part of the energy space and by using this restricted part we can extend our simulations to larger systems and improve accuracy of critical parameters. It is proposed that the extensions of the finite size critical part of the energy space, determining the specific heat, satisfy a scaling law involving the thermal critical exponent. The method is applied successfully for the estimation of the scaling behavior of specific heat of both square and simple cubic Ising lattices. The proposed scaling law is verified by estimating the thermal critical exponent from the finite size behavior of the critical part of the energy space. The density of states (DOS) of the zero-field Ising model on these lattices is obtained via a multi-range Wang-Landau sampling.