Population Annealing with Weighted Averages: A Monte Carlo Method for Rough Free Energy Landscapes

TL;DR

This paper introduces population annealing with weighted averages, a Monte Carlo method that efficiently samples equilibrium states and estimates free energy in systems with complex energy landscapes, demonstrated on spin glasses.

Contribution

It presents a novel Monte Carlo algorithm combining annealing and weighted averaging to improve sampling in rough free energy landscapes, with direct free energy estimation.

Findings

Unbiased observable measurements via weighted averages.

Effective sampling of spin glasses with rough landscapes.

Potential advantages over parallel tempering.

Abstract

The population annealing algorithm introduced by Hukushima and Iba is described. Population annealing combines simulated annealing and Boltzmann weighted differential reproduction within a population of replicas to sample equilibrium states. Population annealing gives direct access to the free energy. It is shown that unbiased measurements of observables can be obtained by weighted averages over many runs with weight factors related to the free energy estimate from the run. Population annealing is well suited to parallelization and may be a useful alternative to parallel tempering for systems with rough free energy landscapes such as spin glasses. The method is demonstrated for spin glasses.