Control of accuracy in the Wang-Landau algorithm

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.

8 pages, 6 figures

References in corpus (5)

• Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error
• Versatile approach to access the low temperature thermodynamics of lattice polymers and proteins
• Optimal Modification Factor and Convergence of the Wang-Landau Algorithm
• Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins
• Convergence of Stochastic Approximation Monte Carlo and modified Wang-Landau algorithms: Tests for the Ising model