Solving the Master Equation for Extremely Long Time Scale Calculations

TL;DR

This paper introduces a novel Monte Carlo method that solves the master equation to accurately simulate magnetic reversal dynamics over extremely long time scales, including microscopic effects in nano-scale systems.

Contribution

A new Monte Carlo approach that solves the master equation for long time scale magnetic dynamics, capable of handling microscopic effects in nano-scale systems.

Findings

Successfully simulated up to 1e50 Monte Carlo steps.

Accurately models microscopic effects like entropy in long time dynamics.

Provides a tool for designing magnetic recording devices.

Abstract

The dynamics of magnetic reversal process plays an important role in the design of the magnetic recording devices in the long time scale limit. In addition to long time scale, microscopic effects such as the entropic effect become important in magnetic nano-scale systems. Many advanced simulation methods have been developed, but few have the ability to simulate the long time scale limit and to accurately model the microscopic effects of nano-scale systems at the same time. We develop a new Monte Carlo method for calculating the dynamics of magnetic reversal at arbitrary long time. For example, actual calculations were performed up to 1e50 Monte Carlo steps. This method is based on microscopic interactions of many constituents and the master equation for magnetic probability distribution function is solved symbolically.