FLAT HISTOGRAM METHOD OF WANG–LANDAU ANDN-FOLD WAY

Ben Jesko Schulz (), Kurt Binder and Marcus Müller
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Ben Jesko Schulz: Institut für Physik, WA331, Johannes Gutenberg Universität, Staudinger Weg 7, D55099 Mainz, Germany
Kurt Binder: Institut für Physik, WA331, Johannes Gutenberg Universität, Staudinger Weg 7, D55099 Mainz, Germany
Marcus Müller: Institut für Physik, WA331, Johannes Gutenberg Universität, Staudinger Weg 7, D55099 Mainz, Germany

International Journal of Modern Physics C (IJMPC), 2002, vol. 13, issue 04, 477-494

Abstract: We present a method for estimating the density of states of a classical statistical model. The algorithm successfully combines the Wang–Landau flat histogram method with theN-fold way in order to improve the efficiency of the original single-spin-flip version. We test our implementation of the Wang–Landau method with the two-dimensional nearest neighbor Ising model for which we determine the tunneling time and the density of states on lattices with sizes up to 50 × 50. Furthermore, we show that our new algorithm performs correctly at right edges of an energy interval over which the density of states is computed. This removes a disadvantage of the original single-spin-flip Wang–Landau method where results showed systematically higher errors in the density of states at right boundaries. In order to demonstrate the improvements made, we compare our data with the detailed numerical tests presented in a study by Wang and Swendsen where the original Wang–Landau method was tested against various other methods, especially the transition matrix Monte Carlo method (TMMC). Finally, we apply our method to a thin Ising film of size 32 × 32 × 6 with antiparallel surface fields. With the density of states obtained from the simulations we calculate canonical averages related to the energy such as internal energy, Gibbs free energy and entropy, but we also sample microcanonical averages during simulations in order to determine canonical averages of the susceptibility, the order parameter and its fourth order cumulant. We compare our results with simulational data obtained from a conventional Monte Carlo algorithm.

Keywords: Monte Carlo simulations; algorithms; phase transitions; Ising model; free energy calculation (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0129183102003243

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