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

Abstract

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 Gri ths 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.

Performance analysis of Cellular Automata HPC implementations

“…For this reason, we focus the analysis in memory related hardware counters. Because we are interested in general CA applications, for automata with more than two states and given by non-integer values, bit packing [34] is not implemented in our code.…”

“…This gives 4 times less memory use. We are interested in complex CA with more than 2 states per cell, and for this reason we do not use bit packing [21,34].…”

Engineering Software for d-Dimensional Simulations with Hyper-Cubic Neighbours

“…In the case of the Ising magnetism model Q = 2 and there are only two allowable states -the quantum spin values "up" and "down." The Potts model [13] extends this to an arbitrary number Q of pseudo-spin variables. The Sznajd opinion model [33] can also use the same structure to represent Q allowable different opinions.…”