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

Tobias Preis, Peter Virnau, Wolfgang Paul, Johannes J. Schneider
Department of Physics, Mathematics and Computer Science, Johannes Gutenberg University of Mainz Staudinger Weg 7, D-55099 Mainz, Germany
Journal of Computational Physics, Vol. 228, No. 12. (01 July 2009), pp. 4468-4477.


   title={GPU accelerated Monte Carlo simulation of the 2D and 3D Ising model},

   author={Preis, T. and Virnau, P. and Paul, W. and Schneider, J.J.},

   journal={Journal of Computational Physics},








The compute unified device architecture (CUDA) is a programming approach for performing scientific calculations on a graphics processing unit (GPU) as a data-parallel computing device. The programming interface allows to implement algorithms using extensions to standard C language. With continuously increased number of cores in combination with a high memory bandwidth, a recent GPU offers incredible resources for general purpose computing. First, we apply this new technology to Monte Carlo simulations of the two dimensional ferromagnetic square lattice Ising model. By implementing a variant of the checkerboard algorithm, results are obtained up to 60 times faster on the GPU than on a current CPU core. An implementation of the three dimensional ferromagnetic cubic lattice Ising model on a GPU is able to generate results up to 35 times faster than on a current CPU core. As proof of concept we calculate the critical temperature of the 2D and 3D Ising model using finite size scaling techniques. Theoretical results for the 2D Ising model and previous simulation results for the 3D Ising model can be reproduced.
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