FLAT HISTOGRAM METHOD OF WANG–LANDAU AND N-FOLD WAY

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 the N-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.