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Bit-Packed Damaged Lattice Potts Model Simulations with CUDA and GPUs

Ken A. Hawick, Mitchell G.B. Johnson
Computer Science, Institute for Information and Mathematical Sciences, Massey University, North Shore 102-904, Auckland, New Zealand
Computational Science Technical Note CSTN-135, 2011

@article{hawick2011bit,

   title={Bit-Packed Damaged Lattice Potts Model Simulations with CUDA and GPUs},

   author={Hawick, K.A. and Johnson, M.G.B.},

   year={2011}

}

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Models such as the Ising and Potts systems lend themselves well to simulating the phase transitions that commonly arise in materials science. A particularly interesting variation is when the material being modelled has lattice defects, dislocations or broken bonds and the material experiences a Griffiths phase. The damaged Potts system consists of a set of multi-valued spins on a lattice, where each site is nominally connected to its nearest neighbouring sites, but with some probability of damage that determines whether individual links are present. We simulate the damaged Potts system on large two dimensional (square) and three dimensional (cubic) lattices, using General Purpose Graphical Processing Units (GPGPU) which are well suited to the intrinisic data parallelism of such models. We employ an unusual bit-packing approach to minimise memory usage and optimise cache performance. We report on computational performance, scalability and some physical measurements used in locating the damage-shifted critical properties.
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