Effective discrete-time dynamics in Monte Carlo simulations

Abstract

The effective discrete-time master equation which governs a Monte Carlo simulation is derived. This equation, which takes explicitly into account the type of algorithm used to update the configurations, when specialized for a spin system and sequential updating, coincides with a similar equation recently proposed in the literature. From this effective master equation it is possible to give theoretical support to previous numerical works concerning the validity of different algorithms for spin updating in the study of kinetic processes. All the analytical results are consistently checked through numerical simulations of a simple exactly solvable model.