FPGA Hardware Acceleration of Monte Carlo Simulations for the Ising Model

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 six times is achieved in comparison to previous FPGA-based published works and almost <inline-formula><tex-math notation="LaTeX">$10^4$</tex-math><alternatives> <inline-graphic xlink:type="simple" xlink:href="ortegazamorano-ieq1-2505725.gif"/></alternatives></inline-formula> 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.

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