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

Abstract

We present sample CUDA programs for the GPU computing of the Swendsen–Wang multi-cluster spin flip algorithm. We deal with the classical spin models; the Ising model, the q-state Potts model, and the classical XY model. As for the lattice, both the 2D (square) lattice and the 3D (simple cubic) lattice are treated. We already reported the idea of the GPU implementation for 2D models (Komura and Okabe, 2012). We here explain the details of sample programs, and discuss the performance of the present GPU implementation for the 3D Ising and XY models. We also show the calculated results of the moment ratio for these models, and discuss phase transitions. Program summaryProgram title: SWspinCatalogue identifier: AERM_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERM_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 5632No. of bytes in distributed program, including test data, etc.: 14688Distribution format: tar.gzProgramming language: C, CUDA.Computer: System with an NVIDIA CUDA enabled GPU.Operating system: System with an NVIDIA CUDA enabled GPU.Classification: 23.External routines: NVIDIA CUDA Toolkit 3.0 or newerNature of problem:Monte Carlo simulation of classical spin systems. Ising, q-state Potts model, and the classical XY model are treated for both two-dimensional and three-dimensional lattices.Solution method:GPU-based Swendsen–Wang multi-cluster spin flip Monte Carlo method. The CUDA implementation for the cluster-labeling is based on the work by Hawick et al. [1] and that by Kalentev et al. [2].Restrictions:The system size is limited depending on the memory of a GPU.Running time:For the parameters used in the sample programs, it takes about a minute for each program. Of course, it depends on the system size, the number of Monte Carlo steps, etc.