Introducing the step Monte Carlo method for simulating dynamic properties

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.