Comparative study of selected parallel tempering methods

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 that exhibit 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, the energies of the ordered and disordered phases, and interface tension. Both methods exhibit similar accuracy at selected sets of modeling parameters.

Intermediate Thermodynamic States Contribute Equally to Free Energy Convergence: A Demonstration with Replica Exchange

We investigate the relationship between the number of intermediate thermodynamic states along a pathway and the precision of free energy estimates. With a sufficient number of states, the asymptotic variance collapses as a function of the total sample size. Our analytical result is corroborated by replica exchange molecular dynamics simulations of model systems in which the neighbor exchange rate exceeds 35%. Precision collapse is also observed in heat capacity estimates based on the multistate Bennett acceptance ratio. In contrast to the relaxation and mean first-passage times, the autocorrelation time of state indices is found to be relevant to free energy convergence.