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High Performance Monte Carlo and Time-Stepping Dynamics for the Classical Spin Heisenberg Model on GPUs

K.A. Hawick, D.P. Playne
Computer Science, Institute for Information and Mathematical Sciences, Massey University, North Shore 102-904, Auckland, New Zealand
CSTN Computational Science Technical Note Series, CSTN-146, 2012

@article{hawick2012high,

   title={High Performance Monte Carlo and Time-Stepping Dynamics for the Classical Spin Heisenberg Model on GPUs},

   author={Hawick, KA and Playne, DP},

   year={2012}

}

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The Heisenberg model of classical spins makes use of both Monte Carlo stochastic dynamics as well as time-integration of its equation of motion. These two schemes have different parallelisation strategies and tradeoffs. We implement both algorithms using a data-parallel approach for Graphical Processing Units (GPUs) and we discuss the resulting performance on various combinations of single and multiple GPU. In addition to studying Monte Carlo dynamical update schemes, we use our fast simulation code to explore the scaling and time correlations of a largescale Heisenberg model system using a high-order numerical integration algorithm, which enables study of accurate spin wave phenomena and time-correlation functions. We also discuss various graphical rendering models to appropriately visualise the spin vectors inside an interactive Heisenberg spin simulation.
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