Optimization of population annealing Monte Carlo for large-scale spin-glass simulations

Barzegar, Amin; Pattison, Christopher A.; Wang, Wenlong; Katzgraber, Helmut G.

doi:10.1103/physreve.98.053308

Cited by 32 publications

(29 citation statements)

References 34 publications

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“…The new algorithm introduced here, which we call EPA, is not based on Markov chains but on the sequential Monte Carlo method. PA was first studied in [53,54] and more recently developed further in [55][56][57][58][59][60][61]. It is based on the initialization of a population of replicas drawn from the equilibrium distribution at high temperatures, which is then subsequently cooled to lower and lower temperatures.…”

Section: Entropic Population Annealingmentioning

confidence: 99%

Estimating the density of states of frustrated spin systems

et al. 2019

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Estimating the density of states (DOS) of systems with rugged free energy landscapes is a notoriously difficult task of the utmost importance in many areas of physics ranging from spin glasses to biopolymers. DOS estimation has also recently become an indispensable tool for the benchmarking of quantum annealers when these function as samplers. Some of the standard approaches suffer from a spurious convergence of the estimates to metastable minima, and these cases are particularly hard to detect. Here, we introduce a sampling technique based on population annealing enhanced with a multi-histogram analysis and report on its performance for spin glasses. We demonstrate its ability to overcome the pitfalls of other entropic samplers, resulting in some cases in large scaling advantages that can lead to the uncovering of new physics. The new technique avoids some inherent difficulties in established approaches and can be applied to a wide range of systems without relevant tailoring requirements. Benchmarking of the studied techniques is facilitated by the introduction of several schemes that allow us to achieve exact counts of the degeneracies of the tested instances.

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Section: Entropic Population Annealingmentioning

confidence: 99%

Estimating the density of states of frustrated spin systems

et al. 2019

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“…This ensures that the system is equilibrated according to the Gibbs distribution at each temperature. For the simulations we use particle-conserving dynamics to ensure that the lattice half filling is kept constant, together with a hybrid temperature schedule linear in β and linear in T [57]. We use the family entropy of population annealing [55] as an equilibration criterion.…”

Section: Simulation Detailsmentioning

confidence: 99%

“…ρ s similarly to ρ f converges at a finite R. The population size at which the convergence is achieved is a function of the number of temperatures N T as well as the number of Metropolis sweeps M . Optimization of PAMC is studied in great detail in the context of spin glasses [56,57] much of which can be carried over to the CG simulations. As an example we show in Figs.…”

Section: Appendix A: Equilibrationmentioning

confidence: 99%

“…In this paper we investigate the phase diagram of the CG model using Monte Carlo simulations in three spatial dimensions. For the finite-temperature simulations we make use of the population annealing Monte Carlo (PAMC) algorithm [53][54][55][56][57] which enables us to thermalize for a broad range of disorder values down to unprecedented low temperatures previously inaccessible. In addition, we argue that the detection of a glass phase requires a four-replica correlation length, as commonly used in spin-glass simulations in a field [58,59].…”

Section: Introductionmentioning

confidence: 99%

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Numerical observation of a glassy phase in the three-dimensional Coulomb glass

et al. 2019

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The existence of an equilibrium glassy phase for charges in a disordered potential with long-range electrostatic interactions has remained controversial for many years. Here we conduct an extensive numerical study of the disordertemperature phase diagram of the three-dimensional Coulomb glass model using population annealing Monte Carlo to thermalize the system down to extremely low temperatures. Our results strongly suggest that, in addition to a charge order phase, a transition to a glassy phase can be observed, consistent with previous analytical and experimental studies.

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“…These results * camey@physics.umass.edu † machta@physics.umass.edu naturally lead to several optimization ideas that we test in the context of the 3D Edwards-Anderson spin glass. Related optimization ideas are explored in [20]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

Analysis and optimization of population annealing

Amey

Machta

2018

Phys. Rev. E

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Population annealing is an easily parallelizable sequential Monte Carlo algorithm that is well suited for simulating the equilibrium properties of systems with rough free-energy landscapes. In this work we seek to understand and improve the performance of population annealing. We derive several useful relations between quantities that describe the performance of population annealing and use these relations to suggest methods to optimize the algorithm. These optimization methods were tested by performing large-scale simulations of the three-dimensional (3D) Edwards-Anderson (Ising) spin glass and measuring several observables. The optimization methods were found to substantially decrease the amount of computational work necessary as compared to previously used, unoptimized versions of population annealing. We also obtain more accurate values of several important observables for the 3D Edwards-Anderson model.

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Optimization of population annealing Monte Carlo for large-scale spin-glass simulations

Cited by 32 publications

References 34 publications

Estimating the density of states of frustrated spin systems

Estimating the density of states of frustrated spin systems

Numerical observation of a glassy phase in the three-dimensional Coulomb glass

Analysis and optimization of population annealing

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