Understanding population annealing Monte Carlo simulations

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2021. Vol. 103. P. 053301-1–053301-24.

Weigel M., Barash L., Shchur L., Janke W.

Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical
physics and it proves to deal well with systems with complex free-energy landscapes. Above all else, it promises
to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest caliber. Here
we study population annealing using as the main example the two-dimensional Ising model, which allows for
particularly clean comparisons due to the available exact results and the wealth of published simulational studies
employing other approaches. We analyze in depth the accuracy and precision of the method, highlighting its
relation to older techniques such as simulated annealing and thermodynamic integration. We introduce intrinsic
approaches for the analysis of statistical and systematic errors and provide a detailed picture of the dependence of
such errors on the simulation parameters. The results are benchmarked against canonical and parallel tempering
simulations.

Keywords: population annealing algorithm, алгоритм отжига популяции, Monte Carlo algorithm, algorithm analysis, алгоритм Монте-Карло, анализ свойств алгоритма