Time Quantified Monte Carlo Method for Long-range Interacting Systems

TL;DR

This paper introduces a novel time quantified Monte Carlo method incorporating stochastic cutoff techniques to efficiently simulate the real-time dynamics of long-range interacting classical spin systems, aligning with the s-LLG equation.

Contribution

The paper presents a new method combining TQMC and SCO techniques, enabling accurate real-time simulation of long-range spin systems and technical improvements to TQMC.

Findings

Method reproduces s-LLG dynamics accurately.

Successfully simulates magnetization reversal processes.

Allows analysis of complex lattice spin systems.

Abstract

We propose a method for simulating the stochastic dynamics of classical spin systems with long-range interactions. The method incorporates the stochastic cutoff (SCO) method, which is originally specialized for simulating equilibrium state, into time quantified Monte Carlo (TQMC) method. We analytically prove that the present method gives the same real-time dynamics with the stochastic Landau-Lifshitz-Gilbert (s-LLG) equation, i.e., both method derives the same Fokker-Planck coefficients. We demonstrate magnetization reversal processes and confirm that the result is in good agreement with the result obtained by s-LLG. Using our method enables us to analyze complicated lattice systems consisting of many spins in a unit cell. Technical improvement of TQMC is also proposed.