FPGA Hardware Acceleration of Monte Carlo Simulations for the Ising Model

Abstract: A two-dimensional Ising model with nearest-neighbors ferromagnetic interactions is implemented in a Field Programmable Gate Array (FPGA) board.Extensive Monte Carlo simulations were carried out using an efficient hardware representation of individual spins and a combined global-local LFSR random number generator. Consistent results regarding the descriptive properties of magnetic systems, like energy, magnetization and susceptibility are obtained while a speed-up factor of approximately 6 times is achieved in comparison to previous FPGA-based published works and almost $10^4$ times in comparison to a standard CPU simulation. A detailed description of the logic design used is given together with a careful analysis of the quality of the random number generator used. The obtained results confirm the potential of FPGAs for analyzing the statistical mechanics of magnetic systems.