# Control of accuracy in the Wang-Landau algorithm

## TL;DR

This paper analyzes the Wang-Landau algorithm, revealing how the eigenvalues of its transition matrix can be used to control the accuracy of density of states estimation, supported by analytic and numerical results.

## Contribution

It introduces a method to control the accuracy of the Wang-Landau algorithm based on eigenvalue analysis, with analytic expressions and numerical validation.

## Key findings

- Eigenvalue difference indicates estimation accuracy
- Analytic expressions derived for 1D Ising model
- Numerical validation on Ising and Potts models

## Abstract

The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of states. Analytic expressions for the matrix elements are given in the case of the one-dimensional Ising model. The proposed method is further confirmed by numerical results for the one-dimensional and two-dimensional Ising models and also the two-dimensional Potts model.