Comparison of the microcanonical population annealing algorithm with the Wang-Landau algorithm

The development of new algorithms for simulations in physics is as important as the development of new analytical methods. In this paper we present a comparison of the recently developed microcanonical population annealing (MCPA) algorithm with the rather mature Wang-Landau algorithm. The comparison is performed on two cases of the Potts model exhibiting a first order phase transition. We compare the simulation results of both methods with exactly known results, including the finite-dimensional dependence of the maximum of the specific heat capacity. We evaluate the Binder cumulant minimum, the ratio of peaks in the energy distribution at the critical temperature, and the energies of the ordered and disordered phases. Both methods exhibit similar accuracy at selected sets of modeling parameters.