Monte Carlo simulation with time step quantification in terms of Langevin dynamics

TL;DR

This paper introduces a time-quantified Monte Carlo algorithm for simulating thermally activated magnetic dynamics, validated against Langevin dynamics and Fokker-Planck solutions, improving interpretation and accuracy of simulation times.

Contribution

A novel Monte Carlo method with time step quantification for magnetic systems, aligning simulation results with analytical and Langevin dynamics.

Findings

Monte Carlo step can be effectively time-quantified.

Simulation results match asymptotic and exact solutions.

Method improves interpretation of Monte Carlo dynamics.

Abstract

For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy axis of the particles. For this model, a comparison of the Monte Carlo method with Langevin dynamics yields new insight in the interpretation of the Monte Carlo process, leading to the implementation of a new algorithm where the Monte Carlo step is time-quantified. The numeric results for the characteristic time of the magnetisation reversal are in excellent agreement with asymptotic solutions which itself are in agreement with the exact numerical results obtained from the Fokker-Planck equation for the Neel-Brown model.