Accuracy and Performance Analysis of the 1/t Wang-Landau Algorithm in the Joint Density of States Estimation

The 1/t Wang-Landau algorithm is analyzed from the viewpoint of execution time and accuracy when it is used in computations of the density of states of a two-dimensional Ising model. We find that the simulation results have a systematic error, the magnitude of which decreases with increasing the lattice size. The relative error has two maxima: the first one is located near the energy of the ground state, and the second maximum corresponds to the value of the internal energy at the critical point. We demonstrate that it is impossible to estimate the execution time of the 1/t Wang-Landau algorithm in advance when simulating large lattices. The reason is that when the final value of the modification factor was reached, the criterion for transition to mode 1/t was not met. The simultaneous calculations of the density of states for energy and magnetization are shown to lead to higher accuracy in estimating statistical moments of internal energy.