Difference of energy density of states in the Wang-Landau algorithm

TL;DR

This paper investigates the convergence properties of the Wang-Landau algorithm by analyzing the difference in the density of states, proposing a new estimator for errors, and examining phase transition behaviors.

Contribution

It introduces the difference of density of states as a convergence estimator and connects it with phase transition analysis, providing a new method to assess transition order.

Findings

The difference of density of states effectively estimates convergence errors.

The 1/t algorithm's behavior is clarified through this estimator.

A procedure to determine the order of phase transitions is proposed.

Abstract

Paying attention to the difference of density of states, \Delta ln g(E) = ln g(E+\Delta E) - ln g(E), we study the convergence of the Wang-Landau method. We show that this quantity is a good estimator to discuss the errors of convergence, and refer to the $1/t$ algorithm. We also examine the behavior of the 1st-order transition with this difference of density of states in connection with Maxwell's equal area rule. A general procedure to judge the order of transition is given.