Introducing the step Monte Carlo method for simulating dynamic properties

TL;DR

This paper introduces step Monte Carlo (sMC), a simple modification to traditional Monte Carlo methods that enables simulation of far-from-equilibrium dynamics and provides insights into system properties without extra parameters.

Contribution

The paper presents the sMC algorithm, which uses activation energy for acceptance probability, allowing dynamic property simulation without additional input parameters.

Findings

sMC accurately reproduces dynamic properties of a spin model

Comparison with stochastic Landau-Lifshitz-Gilbert confirms correctness

Potential applications include atom dynamics, diffusion, and crystal growth

Abstract

In this work, we introduce a simple modification of the Monte Carlo algorithm, which we call step Monte Carlo (sMC). The sMC approach allows to simulate processes far from equilibrium and obtain information about the dynamic properties of the system under investigation. In the approach proposed here the probability of accepting the final (trial) state depends on the activation energy, not on the relative energy between the final and initial state. This barrier height is probed on an ongoing basis, by generating intermediate states along the path connecting the initial and trial positions. Importantly, to calculate the activation energy, our model only requires knowledge of the Hamiltonian without having to introduce additional input parameters such as transition rates etc. The details of sMC are explained for the case of a simple spin model. The comparison of its results with the ones obtained within the frame of stochastic Landau-Lifshitz-Gilbert indicates the correctness of sMC. In our opinion, the proposed here method can be applied to simulate other processes, for example dynamics of classical atoms and complex fluids, diffusion, nucleation, surface adsorption and crystal growth processes.