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 (12)

• An efficient, multiple range random walk algorithm to calculate the density of states
• Determining the density of states for classical statistical models: A random walk algorithm to produce a flat histogram
• Fast Algorithm to Calculate Density of States
• Understanding and Improving the Wang-Landau Algorithm
• 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
• Convergence and Refinement of the Wang-Landau Algorithm
• 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
• Estimation of critical behavior from the density of states in Classical Statistical Models
• Universality aspects of the 2d random-bond Ising and 3d Blume-Capel models
• Convergence of Stochastic Approximation Monte Carlo and modified Wang-Landau algorithms: Tests for the Ising model

Cited by in corpus (9)

• A mapping space Odyssey: characterising the statistical and metric properties of reduced representations of macromolecules
• Estimating the Density of States of Frustrated Spin Systems
• A portable and flexible implementation of the Wang--Landau algorithm in order to determine the Density of States
• Blume-Capel model analysis with microcanonical population annealing method
• On properties of the Wang--Landau algorithm
• Comparison of the microcanonical population annealing algorithm with the Wang-Landau algorithm
• Flat histogram method comparison on 2D Ising Model
• Efficient sampling using Macrocanonical Monte Carlo and density of states mapping
• On the mixing time in the Wang-Landau algorithm