GPU-based single-cluster algorithm for the simulation of the Ising model

Yukihiro Komura, Yutaka Okabe
Department of Physics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
arXiv:1110.0899v1 [physics.comp-ph] (5 Oct 2011)


   author={Komura, Yukihiro and Okabe, Yutaka},

   title={"{GPU-based single-cluster algorithm for the simulation of the Ising model}"},

   journal={ArXiv e-prints},




   keywords={Computational Physics},




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We present the GPU calculation with the common unified device architecture (CUDA) for the Wolff single-cluster algorithm of the Ising model. Proposing an algorithm for a quasi-block synchronization, we realize the Wolff single-cluster Monte Carlo simulation with CUDA. We perform parallel computations for the newly added spins in the growing cluster. As a result, the GPU calculation speed for the two-dimensional Ising model at the critical temperature with the linear size L=4096 is 5.60 times as fast as the calculation speed on a current CPU core. For the three-dimensional Ising model with the linear size L=256, the GPU calculation speed is 7.90 times as fast as the CPU calculation speed. The idea of quasi-block synchronization can be used not only in the cluster algorithm but also in many fields where the synchronization of all threads is required.
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