Understanding population annealing Monte Carlo simulations

TL;DR

This paper provides a comprehensive analysis of population annealing Monte Carlo, demonstrating its accuracy, precision, and parallel scalability in simulating the 2D Ising model, and compares it with other established methods.

Contribution

It introduces new intrinsic methods for analyzing errors in population annealing and benchmarks its performance against other Monte Carlo techniques.

Findings

Population annealing achieves high accuracy in the 2D Ising model.

The method exhibits excellent parallel scalability.

Error analysis depends systematically on simulation parameters.

Abstract

Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found 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 calibre. 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.