Weighted averages in population annealing: analysis and general framework

TL;DR

This paper introduces a generalized framework for weighted averaging in population annealing, demonstrating its unbiased estimators and applying it to complex systems like spin glasses with extensive numerical validation.

Contribution

It extends population annealing with weighted averaging to a broader class of observables and provides rigorous proofs of estimator unbiasedness for finite systems.

Findings

Weighted averaging reduces errors in population annealing.

The estimators are asymptotically unbiased for arbitrary distributions.

Numerical results confirm the effectiveness in spin systems.

Abstract

Population annealing is a powerful sequential Monte Carlo algorithm designed to study the equilibrium behavior of general systems in statistical physics through massive parallelism. In addition to the remarkable scaling capabilities of the method, it allows for measurements to be enhanced by weighted averaging, admitting to reduce both systematic and statistical errors based on independently repeated simulations. We give a self-contained introduction to population annealing with weighted averaging, generalize the method to a wide range of observables such as the specific heat and magnetic susceptibility and rigorously prove that the resulting estimators for finite systems are asymptotically unbiased for essentially arbitrary target distributions. Numerical results based on more than $10^7$ independent population annealing runs of the two-dimensional Ising ferromagnet and the Edwards-Anderson Ising spin glass are presented in depth. In the latter case, we also discuss efficient ways of measuring spin overlaps in population annealing simulations.