Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error

Details Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error

2007-02-19

arxiv.org/abs/cond-mat/0702414v3

Physics

Condensed Matter

Statistical Mechanics

7 pages, 5 figures

Scientific paper

10.1063/1.2803061

In this work we present a theoretical analysis of the convergence of the Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced years ago to calculate the density of states in statistical models. We study the dynamical behavior of the error in the calculation of the density of states.We conclude that the source of the saturation of the error is due to the decreasing variations of the refinement parameter. To overcome this limitation, we present an analytical treatment in which the refinement parameter is scaled down as a power law instead of exponentially. An extension of the analysis to the N-fold way variation of the method is also discussed.

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