Berlin 2008 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 29: Poster II

DY 29.10: Poster

Donnerstag, 28. Februar 2008, 16:00–18:00, Poster C

Equilibrium properties of the Wang-Landau algorithm — •Mathias Aust, Elmar Bittner, and Wolfhard Janke — Institut für Theoretische Physik, Universität Leipzig, Postfach 100920, 04009 Leipzig, Germany

The Wang-Landau method is generally considered to be an efficient Monte Carlo algorithm. It certainly is an easily implemented method to determine the density of states which is required for simulations on generalized ensembles such as multicanonical simulations. But since the Wang-Landau method uses strongly fluctuating, time-dependent weights instead of a fixed ensemble, there is no mathematical proof that the method yields reliable results.

This work provides a scheme to evaluate statistical data from time series lacking a fixed ensemble. The scheme is applied to Wang-Landau simulations of the two-dimensional Ising model measuring the energy and magnetization. The results are compared with data from exact enumerations on small lattices as well as with the exact Beale solution and magnetization data from multicanonical simulations for lattice sizes up to 64 × 64 to check for systematic errors of the algorithm.

Additionally, the Wang-Landau method is combined with the Transition Matrix evaluation scheme by Wang and Swendsen to find a good working estimate of the density of states even faster.