On properties of the WangLandau algorithm
Abstract
We review recent advances in the analysis of the WangLandau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the WangLandau probability. Properties of the TMES can explain some features of the WangLandau algorithm, for example, the flatness of the histogram. We show that the WangLandau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of the WangLandau algorithm consists of two simulation stages: the original WangLandau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.
 Publication:

Journal of Physics Conference Series
 Pub Date:
 June 2019
 DOI:
 10.1088/17426596/1252/1/012010
 arXiv:
 arXiv:1808.09251
 Bibcode:
 2019JPhCS1252a2010S
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 31st Annual Worskshop "Recent Developments in Computer Simulational Studies in Condensed Matter Physics", Center for Simulational Physics, University of Georgia, February 1923, 2018