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

TL;DR

This paper compares the microcanonical population annealing algorithm with the Wang-Landau algorithm in simulating Potts models with first-order phase transitions, evaluating their accuracy against known results.

Contribution

It provides a direct comparison of MCPA and Wang-Landau algorithms on complex phase transition models, highlighting their similar accuracy.

Findings

Both algorithms show comparable accuracy in simulations.

The comparison includes key thermodynamic quantities and phase transition indicators.

Results validate the effectiveness of MCPA relative to the established Wang-Landau method.

Abstract

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.