Population Annealing and Its Application to a Spin Glass

Hukushima, Koji; Iba, Yukito

doi:10.1063/1.1632130

Cited by 79 publications

(93 citation statements)

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“…The use of GPGPU for scientific applications is of interest for instance in the stochastic simulations of spin models [1][2][3][4]. Our main goal is to incorporate the GPU-accelerated computing in the population annealing (PA) method proposed by Hukushima and Iba [5]. In section 2, the principles of the PA algorithm are reviewed.…”

Section: Introductionmentioning

confidence: 99%

GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice

Borovský

Weigel

Barash

et al. 2016

EPJ Web of Conferences

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Abstract. The population annealing algorithm is a novel approach to study systems with rough free-energy landscapes, such as spin glasses. It combines the power of simulated annealing, Boltzmann weighted differential reproduction and sequential Monte Carlo process to bring the population of replicas to the equilibrium even in the low-temperature region. Moreover, it provides a very good estimate of the free energy. The fact that population annealing algorithm is performed over a large number of replicas with many spin updates, makes it a good candidate for massive parallelism. We chose the GPU programming using a CUDA implementation to create a highly optimized simulation. It has been previously shown for the frustrated Ising antiferromagnet on the stacked triangular lattice with a ferromagnetic interlayer coupling, that standard Markov Chain Monte Carlo simulations fail to equilibrate at low temperatures due to the effect of kinetic freezing of the ferromagnetically ordered chains. We applied the population annealing to study the case with the isotropic intra-and interlayer antiferromagnetic coupling (J 2 /|J 1 | = −1). The reached ground states correspond to non-magnetic degenerate states, where chains are antiferromagnetically ordered, but there is no long-range ordering between them, which is analogical with Wannier phase of the 2D triangular Ising antiferromagnet.

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Section: Introductionmentioning

confidence: 99%

GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice

Borovský

Weigel

Barash

et al. 2016

EPJ Web of Conferences

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“…The population annealing method was first discussed by Iba [5] in the general context of population-based algorithms and later applied to spin glasses by Hukushima and Iba [6]. More recently, Machta [7] used a method that avoids the recording of weight functions through population control in every step.…”

Section: Algorithmmentioning

confidence: 99%

“…The resampling process in step 2 can be realized in different ways [6,7]. Here we use the following approach [11].…”

Section: Population Annealingmentioning

confidence: 99%

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GPU accelerated population annealing algorithm

Barash

Weigel

Borovský

et al. 2017

Computer Physics Communications

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Population annealing is a promising recent approach for Monte Carlo simulations in statistical physics, in particular for the simulation of systems with complex free-energy landscapes. It is a hybrid method, combining importance sampling through Markov chains with elements of sequential Monte Carlo in the form of population control. While it appears to provide algorithmic capabilities for the simulation of such systems that are roughly comparable to those of more established approaches such as parallel tempering, it is intrinsically much more suitable for massively parallel computing. Here, we tap into this structural advantage and present a highly optimized implementation of the population annealing algorithm on GPUs that promises speed-ups of several orders of magnitude as compared to a serial implementation on CPUs. While the sample code is for simulations of the 2D ferromagnetic Ising model, it should be easily adapted for simulations of other spin models, including disordered systems. Our code includes implementations of some advanced algorithmic features that have only recently been suggested, namely the automatic adaptation of temperature steps and a multi-histogram analysis of the data at different temperatures. The program calculates the internal energy, specific heat, several magnetization moments, entropy and free energy of the 2D Ising model on square lattices of edge length L with periodic boundary conditions as a function of inverse temperature β. Solution method: The code uses population annealing, a hybrid method combining Markov chain updates with population control. The code is implemented for NVIDIA GPUs using the CUDA language and employs advanced techniques such as multi-spin coding, adaptive temperature steps and multi-histogram reweighting. Restrictions: The system size and size of the population of replicas are limited depending on the memory of the GPU device used. Unusual features: Additional comments: Code repository at https://github.com/LevBarash/PAising. Running time: For the default parameter values used in the sample programs, L = 64, θ = 100, β0 = 0, β f = 1, ∆β = 0.005, R = 20 000, a typical run time on an NVIDIA Tesla K80 GPU is 151 seconds for the single spin coded (SSC) and 17 seconds for the multi-spin coded (MSC) program (see Sec. 2 for a description of these parameters). PROGRAM SUMMARY

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“…12) Our previous study 13) has revealed several new types of exact equalities between nonequilibrium processes and equilibrium properties of spin glasses by use of the gauge symmetry in addition to the above-mentioned nonequilibrium relations. In that paper, we have considered an application of the method of gauge transformation to the Jarzynski equality to shed new light on the possibilities to use a relatively unconventional sampling method, annealed importance sampling or its improvement known as the population annealing, [14][15][16] in the theoretical studies of spin glasses. These methods use a relation analogous to the Jarzynski equality while changing the temperature similarly to simulated annealing 17) and show outstanding performance comparable to the exchange Monte Carlo method.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium Work on Spin Glasses in Longitudinal and Transverse Fields

2011

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We derive a number of exact relations between equilibrium and nonequilibrium quantities for spin glasses in external fields using the Jarzynski equality and gauge symmetry. For randomly-distributed longitudinal fields, a lower bound is established for the work done on the system in nonequilibrium processes, and identities are proven to relate equilibrium and nonequilibrium quantities. In the case of uniform transverse fields, identities are proven between physical quantities and exponentiated work done to the system at different parts of the phase diagram with the context of quantum annealing in mind. Additional relations are given, which relate the exponentiated work in quantum and simulated (classical) annealing. It is also suggested that the Jarzynski equality may serve as a guide to develop a method to perform quantum annealing under non-adiabatic conditions.

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Population Annealing and Its Application to a Spin Glass

Cited by 79 publications

References 0 publications

GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice

GPU-Accelerated Population Annealing Algorithm: Frustrated Ising Antiferromagnet on the Stacked Triangular Lattice

GPU accelerated population annealing algorithm

Nonequilibrium Work on Spin Glasses in Longitudinal and Transverse Fields

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