Weighted averages in population annealing: analysis and general framework

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.

arXiv comment21 pages, 13 figures, 3 tables, RevTeX4.2

References in corpus (15)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• A Cluster Monte Carlo Algorithm for 2-Dimensional Spin Glasses
• Population Annealing with Weighted Averages: A Monte Carlo Method for Rough Free Energy Landscapes
• Population Monte Carlo algorithms
• Population annealing: Theory and application in spin glasses
• GPU accelerated population annealing algorithm
• Chaos in spin glasses revealed through thermal boundary conditions
• Understanding population annealing Monte Carlo simulations
• Optimization of population annealing Monte Carlo for large-scale spin-glass simulations
• Analysis and Optimization of Population Annealing
• Accelerating molecular dynamics simulations with population annealing
• Population Annealing Simulations of a Binary Hard Sphere Mixture
• Numerically exact correlations and sampling in the two-dimensional Ising spin glass
• Equilibrium Microcanonical Annealing for First-Order Phase Transitions
• Massively parallel simulations for disordered systems

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