Stochastic scaling of the time step length in a full-scale Monte Carlo Potts model

Abstract

Grain growth is a fundamental reaction in polycrystalline solid materials that significantly influences various material properties. The Monte Carlo Potts model is notable for its simple algorithm and low computational cost, effectively capturing fundamental grain growth kinetics and providing quantitative predictions. Its realistic time assignment scheme relies on experimental information and simulation resolution. This can result in excessively short simulation time step, significantly increasing the required simulation time and limiting its practical use in real-world materials design. Here, we propose a novel scheme to control the actual length of a Monte Carlo step based on the fundamental physical principles underlying the Monte Carlo algorithm. The simulation results were confirmed to be consistent after the timescale adjustment. Furthermore, the present approach provides a reasonable way to determine the length of a Monte Carlo step in complex simulations where multiple Monte Carlo Potts models for different reaction kinetics are included. The present approach is expected to broaden the applicability of the Monte Carlo Potts model for practical processes in the real world.