Wang-Landau algorithm: A theoretical analysis of the saturation of the error
Abstract
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.
- Publication:
-
Journal of Chemical Physics
- Pub Date:
- November 2007
- DOI:
- 10.1063/1.2803061
- arXiv:
- arXiv:cond-mat/0702414
- Bibcode:
- 2007JChPh.127r4105B
- Keywords:
-
- 05.40.Fb;
- 05.50.+q;
- Random walks and Levy flights;
- Lattice theory and statistics;
- Condensed Matter - Statistical Mechanics
- E-Print:
- 7 pages, 5 figures