Thinning algorithms for the Monte Carlo simulation of kinetic Ising models

The thinning method for numerically generating the arrival times of nonhomogeneous Poisson processes (NHPPs) has been adapted to accelerate Monte Carlo simulations of kinetic Ising models (KIMs) with Glauber spin-flip dynamics. The performance of the proposed algorithms is illustrated through simulations of the decay of metastable states in stationary KIMs and of the hysteresis of KIMs in a periodic external field. The thinning is implemented using piecewise-constant majorizing functions that bound from above or are equal to the NHPP rate. In favorable cases, this approach enables the simulations of hysteresis at frequencies in the tens of nanohertz and the decay of metastable states with lifetimes many orders magnitude longer than those accessible in previous simulations. The simulated results show good agreement with low-temperature analytical theories. Although algorithmic acceleration becomes more pronounced at lower temperatures, hysteresis has been simulated at moderately low temperatures of practical relevance, ranging from below room temperature up to values used in hyperthermia applications.