Understanding population annealing Monte Carlo simulations

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.

26 pages, 23 figures

References in corpus (4)

• Comparing Monte Carlo methods for finding ground states of Ising spin glasses: population annealing, simulated annealing and parallel tempering
• Cross-correlations in scaling analyses of phase transitions
• Stratification and Optimal Resampling for Sequential Monte Carlo
• Algorithm for the replica redistribution in the implementation of parallel annealing method on the hybrid supercomputer architecture

Cited by in corpus (14)

• Model-Free Data-Driven Inference in Computational Mechanics
• Weighted averages in population annealing: analysis and general framework
• An effective introduction to the Markov Chain Monte Carlo method
• Optimal schedules for annealing algorithms
• Blume-Capel model analysis with microcanonical population annealing method
• Comparison of the microcanonical population annealing algorithm with the Wang-Landau algorithm
• Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models
• Quantum-enhanced Markov Chain Monte Carlo for systems larger than your Quantum Computer
• Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions
• Stochastic parameter optimization analysis of dynamical quantum critical phenomena in long-range transverse-field Ising chain
• Ground state interface exponents of the diluted Sherrington-Kirkpatrick spin glass
• Frustrated Ising model on the honeycomb lattice: Metastability and universality
• Quasi-exact ground-state algorithm for the random-field Potts model
• Resampling schemes in population annealing -- numerical results