CUDA programs for the GPU computing of the Swendsen–Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

Komura, Yukihiro; Okabe, Yutaka

doi:10.1016/j.cpc.2013.10.029

Cited by 17 publications

(10 citation statements)

References 23 publications

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“…where S r =(cos θ r , sin θ r ) denotes a planar spin vector with unit length at site r and the summation runs over pairs of nearest neighboring sites on a simple-cubic lattice. As listed in Table II [14]. Albeit these estimates are all based on Monte Carlo simulations, they are not completely consistent with each other.…”

Section: Modelsmentioning

confidence: 83%

High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class

Sun

et al. 2019

Phys. Rev. B

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We present a worm-type Monte Carlo study of several typical models in the three-dimensional (3D) U(1) universality class, which include the classical 3D XY model in the directed flow representation and its Villain version, as well as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the imaginary-time world-line representation. From the topology of the configurations on a torus, we sample the superfluid stiffness ρs and the dimensionless wrapping probability R. From the finite-size scaling analyses of ρs and of R, we determine the critical points as Tc(XY) = 2.201 844 1(5) and Tc(Villain) = 0.333 067 04 (7) and (t/U )c(BH) = 0.059 729 1(8), where T is the temperature for the classical models, and t and U are respectively the hopping and on-site interaction strength for the BH model. The precision of our estimates improves significantly over that of the existing results. Moreover, it is observed that at criticality, the derivative of a wrapping probability with respect to T suffers from negligible leading corrections and enables a precise determination of the correlation length critical exponent as ν = 0.671 83(18). In addition, the critical exponent η is estimated as η = 0.038 53(48) by analyzing a susceptibility-like quantity. We believe that these numerical results would provide a solid reference in the study of classical and quantum phase transitions in the 3D U(1) universality, including the recent development of the conformal bootstrap method.

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Section: Modelsmentioning

confidence: 83%

High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class

Sun

et al. 2019

Phys. Rev. B

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“…If a spatial decomposition strategy is to be used, it must be applied to the cluster selection and cluster identification. This has been achieved for Swendsen/Wang and Wolff algorithms for lattice spin models recently [12,13], and these algorithms have been implemented with efficiency gains on GPUs.…”

Section: Introductionmentioning

confidence: 99%

Parallelized event chain algorithm for dense hard sphere and polymer systems

Kampmann

Boltz

Kierfeld

2015

Journal of Computational Physics

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We combine parallelization and cluster Monte Carlo for hard sphere systems and present a parallelized event chain algorithm for the hard disk system in two dimensions. For parallelization we use a spatial partitioning approach into simulation cells. We find that it is crucial for correctness to ensure detailed balance on the level of Monte Carlo sweeps by drawing the starting sphere of event chains within each simulation cell with replacement. We analyze the performance gains for the parallelized event chain and find a criterion for an optimal degree of parallelization. Because of the cluster nature of event chain moves massive parallelization will not be optimal. Finally, we discuss first applications of the event chain algorithm to dense polymer systems, i.e., bundle-forming solutions of attractive semiflexible polymers.

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“…On the other hand, the MC simulation methods are based on inter-atomic properties, and therefore, modeling of mesoscopic systems results in significant consumption of computational resources. This problem can be solved using parallelization of the MC algorithm [ 20 , 21 ]. Unfortunately, in order to study magnetization processes of ferromagnetic systems, it is necessary to utilize one of the cluster MC methods, and therefore, the possible parallelization is rather problematic.…”

Section: Introductionmentioning

confidence: 99%

From Atomic Level to Large-Scale Monte Carlo Magnetic Simulations

et al. 2020

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This paper refers to Monte Carlo magnetic simulations for large-scale systems. We propose scaling rules to facilitate analysis of mesoscopic objects using a relatively small amount of system nodes. In our model, each node represents a volume defined by an enlargement factor. As a consequence of this approach, the parameters describing magnetic interactions on the atomic level should also be re-scaled, taking into account the detailed thermodynamic balance as well as energetic equivalence between the real and re-scaled systems. Accuracy and efficiency of the model have been depicted through analysis of the size effects of magnetic moment configuration for various characteristic objects. As shown, the proposed scaling rules, applied to the disorder-based cluster Monte Carlo algorithm, can be considered suitable tools for designing new magnetic materials and a way to include low-level or first principle calculations in finite element Monte Carlo magnetic simulations.

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CUDA programs for the GPU computing of the Swendsen–Wang multi-cluster spin flip algorithm: 2D and 3D Ising, Potts, and XY models

Cited by 17 publications

References 23 publications

High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class

High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class

Parallelized event chain algorithm for dense hard sphere and polymer systems

From Atomic Level to Large-Scale Monte Carlo Magnetic Simulations

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