Accelerating Monte Carlo Simulations of Two-Dimensional Spin Models using GPUs

Utilizing the vast computational power of Graphics Processing Units, we develop novel algorithms in both OpenCL and CUDA to study the statistical mechanical properties of two-dimensional spin models. Our basic technique is the general Markov chain Monte Carlo method which uses a Metropolis-Hastings step. In contrast to the popular method of checkerboard updates, we have devised an unconventional procedure that traverses rows to generate the spin configurations. This special implementation allows us to simulate large system sizes (~ 10^9 spins) and, when tested on our fastest GPU, produces an average time per spin-flip of 0.005 ns with a speed-up factor of 600 compared to an optimized single-core CPU algorithm. We test the performance characteristics of our techniques for simulating 2D spin models such as the Ising, XY, and Potts on hexagonal and square lattices. Finally, as a theoretical proof of our computational concept we present critical temperatures of the models based on finite-size scaling methods.