Monte Carlo simulation of the Ising model on FPGA

Two-dimensional Ising lattices are simulated on a field programmable gate array (FPGA) based system. Multiple spins are updated at each FPGA clock, leading to a linear increase of simulation time with the lattice size. A hybrid random number generator is designed and shown to have a better statistical quality than the tested pseudorandom generators. For a 1024 × 1024 Ising lattice, speedups of 1518× over single CPU, 11.8× over single GPU, and 1.5× over previously reported FPGA based simulation systems are achieved. Simulations of 1024 × 1024 Ising models with sampling periods up to 4.2 million Monte Carlo sweeps (MCS) and total spin updates of 17.2 billion MCS are carried out to study autocorrelation effects at the transition temperature. The mean magnetization is shown to converge to a stable value when the sampling period is reaching 105 MCS, and the standard deviation of the mean is shown to be described better with an equation from Kikuchi and Ito.