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

Area of Science:

• Computational Physics
• Statistical Mechanics
• Algorithm Development

Background:

• Developing new algorithms is crucial for advancing physics simulations.
• The microcanonical population annealing (MCPA) algorithm is a recent development.
• The Wang-Landau algorithm is a mature and widely used simulation method.

Purpose of the Study:

• To compare the performance and accuracy of the MCPA algorithm against the Wang-Landau algorithm.
• To evaluate both algorithms on systems exhibiting first-order phase transitions, specifically the Potts model.
• To validate simulation results against exactly known solutions.

Main Methods:

• Simulation of two cases of the Potts model, known to exhibit first-order phase transitions.
• Application of both the microcanonical population annealing (MCPA) and Wang-Landau algorithms.
• Comparison of simulation results with exact solutions, including analysis of specific heat capacity, Binder cumulant, energy distributions, and interface tension.

Main Results:

• Both MCPA and Wang-Landau algorithms demonstrated comparable accuracy for the selected Potts model cases.
• Key physical quantities such as Binder cumulant minimum and interface tension were evaluated.
• The finite-dimensional dependence of the specific heat capacity maximum was analyzed for both methods.

Conclusions:

• The recently developed MCPA algorithm offers accuracy comparable to the established Wang-Landau algorithm for simulating first-order phase transitions in the Potts model.
• Both algorithms are effective tools for studying critical phenomena in statistical mechanics.
• Further research may explore MCPA's applicability to a broader range of complex physical systems.