Ken A. Hawick and Mitchell G.B. Johnson
Potts, GPU, bit-packing, phase transition, Griffiths phase
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. The damaged Potts system on large two dimensional (square) and three dimensional (cubic) lattices is simulated using General Purpose Graphical Processing Units (GPGPU) which are well suited to the intrinsic data parallelism of such models. An unusual bit-packing approach is employed to minimise memory usage and optimise cache performance. A discussion is given on computational performance, scalability and some physical measurements used in locating the damage-shifted critical properties.
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