Study on the modification factor of Wang-Landau sampling for computational science

Wang-Landau Monte Carlo sampling is the most efficient method in obtaining the density of states as a function of energy E ( g ( E )). In Wang-Landau sampling, the most important concept to calculate g ( E ) more efficiently is the modification factor f. For the systematic study of the modification factor of Wang-Landau sampling, the density of states g i ( E ) of the Ising model on a 20 × 20 square lattice is obtained for a sequence of modification factors f i = exp[2 1− i ] ( i = 1 ~ 30). The sampling results are evaluated by using the traditional maximum entropy and the first partition function zero (a more sensitive indicator) for the first time. With both speed and accuracy considered, the best choice of the final modification factor f final can be f final − 1 = 10 −7 . If one wants to save simulation time, a clever choice is f final − 1 = 10 −4 , yielding a valuable estimate of g ( E ).