Thinning algorithms for the Monte Carlo simulation of kinetic Ising models

TL;DR

This paper introduces thinning algorithms adapted for Monte Carlo simulations of kinetic Ising models, significantly improving efficiency in simulating metastable decay and hysteresis at low temperatures.

Contribution

The paper develops and demonstrates thinning algorithms tailored for kinetic Ising models, enabling faster simulations of rare events and hysteresis phenomena.

Findings

Simulations of metastable decay extend to longer lifetimes.

Hysteresis at very low frequencies is achievable.

Results align well with low-temperature analytic theories.

Abstract

The thinning method for numerical generation of the nonhomogeneous Poisson process (NHPP) arrival times has been adapted to accelerate Monte Carlo simulations of the kinetic Ising models (KIMs) with the Glauber spin-flip dynamics. The performance of the suggested algorithms has been illustrated by simulation of the decay of metastable states in stationary KIMs and of hysteresis in KIMs in a periodic external field. The thinning has been implemented by means of piecewise constant majorizing functions which exceed or are equal to NHPP rate. It has been shown that in favorable cases the use of thinning makes possible the simulations of hysteresis at frequencies in tens nanohertz and the decay of metastable states with lifetimes by many orders exceeding those in previous simulations. Good agreement of simulated results with low-temperature analytic theories has been established. Though the algorithm acceleration has been shown to enhance with lowering temperature, the hysteresis has been simulated at moderately low temperatures of practical interest estimated to cover the range from below the room temperature up to temperatures used in hyperthermia applications.