GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

Preis, Tobias; Virnau, Peter; Paul, Wolfgang; Schneider, Jan

doi:10.1016/j.jcp.2009.03.018

Cited by 296 publications

(251 citation statements)

References 24 publications

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“…[73] and based on previous implementations in Refs. [74,75]. Most simulations were performed using the CUDA (compute unified device architecture) framework provided by Nvidia, but implementations using OpenCL have also been tested.…”

Section: Appendixmentioning

confidence: 99%

Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model

et al. 2014

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As a generic example for crystals where the crystal-fluid interface tension depends on the orientation of the interface relative to the crystal lattice axes, the nearest neighbor Ising model on the simple cubic lattice is studied over a wide temperature range, both above and below the roughening transition temperature. Using a thin film geometry Lx × Ly × Lz with periodic boundary conditions along the z-axis and two free Lx × Ly surfaces at which opposing surface fields ±H1 act, under conditions of partial wetting, a single planar interface inclined under a contact angle θ < π/2 relative to the yz-plane is stabilized. In the y-direction, a generalization of the antiperiodic boundary condition is used that maintains the translational invariance in y-direction despite the inhomogeneity of the magnetization distribution in this system. This geometry allows a simultaneous study of the angle-dependent interface tension, the contact angle, and the line tension (which depends on the contact angle, and on temperature). All these quantities are extracted from suitable thermodynamic integration procedures. In order to keep finite size effects as well as statistical errors small enough, rather large lattice sizes (of the order of 46 million sites) are found necessary, availability of very efficient code implementation of graphics processing units (GPUs) was crucial for the feasibility of this study.

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Section: Appendixmentioning

confidence: 99%

Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model

et al. 2014

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“…Therefore, the focus has been redirected to the multicore solutions. However, even with this approach the performance of the CPUs has been increased by a factor of 16 1 . On the other hand, in the same time frame the single precision performance of the NVIDIA GPUs has grown by an order of two 2 .…”

Section: Introductionmentioning

confidence: 99%

“…It takes a lot of thought and caution to incorporate all of this to create a highly optimized CUDA program. 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].…”

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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“…[57][58][59] However, such methods have gained popularity in the physics and mathematics communities and show great promise for future studies, especially with the emergence of the graphics card as a powerful platform for particle simulations and image processing. [60][61][62] Moreover, there has been a marked increase in the ability to synthesize a stunning array of faceted (nonconvex) particles, 15,26,27,[31][32][33][34][35] as well as a large improvement in the level of control with which such particles can be prepared. 28 This has led to particular interest from the materials science community in these overlap algorithms to perform simulations on nanoparticle and colloid systems.…”

Section: Hard-particle Overlap Algorithmsmentioning

confidence: 99%

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

Graaf

Filion

Maréchal

et al. 2012

The Journal of Chemical Physics

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In this paper, we describe the way to set up the floppy-box Monte Carlo (FBMC) method [L. Filion, M. Marechal, B. van Oorschot, D. Pelt, F. Smallenburg, and M. Dijkstra, Phys. Rev. Lett. 103, 188302 (2009)] to predict crystal-structure candidates for colloidal particles. The algorithm is explained in detail to ensure that it can be straightforwardly implemented on the basis of this text. The handling of hard-particle interactions in the FBMC algorithm is given special attention, as (soft) short-range and semi-long-range interactions can be treated in an analogous way. We also discuss two types of algorithms for checking for overlaps between polyhedra, the method of separating axes and a triangular-tessellation based technique. These can be combined with the FBMC method to enable crystal-structure prediction for systems composed of highly shape-anisotropic particles. Moreover, we present the results for the dense crystal structures predicted using the FBMC method for 159 (non)convex faceted particles, on which the findings in [J. de Graaf, R. van Roij, and M. Dijkstra, Phys. Rev. Lett. 107, 155501 (2011)] were based. Finally, we comment on the process of crystalstructure prediction itself and the choices that can be made in these simulations.

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GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model

Cited by 296 publications

References 24 publications

Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model

Anisotropic interfacial tension, contact angles, and line tensions: A graphics-processing-unit-based Monte Carlo study of the Ising model

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

Crystal-structure prediction via the Floppy-Box Monte Carlo algorithm: Method and application to hard (non)convex particles

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