A functional calculus for the magnetization dynamics

TL;DR

This paper introduces a functional calculus framework to derive evolution equations for magnetization moments under stochastic fields, applicable to both Markovian and non-Markovian dynamics, with extensive numerical validation.

Contribution

It develops a general formalism for stochastic magnetization dynamics and tests hierarchy closure assumptions through numerical studies.

Findings

Hierarchy of evolution equations derived for magnetization moments

Closure assumptions validated by numerical simulations

Applicable to both Markovian and non-Markovian systems

Abstract

A functional calculus approach is applied to the derivation of evolution equations for the moments of the magnetization dynamics of systems subject to stochastic fields. It allows us to derive a general framework for obtaining the master equation for the stochastic magnetization dynamics, that is applied to both, Markovian and non-Markovian dynamics. The formalism is applied for studying different kinds of interactions, that are of practical relevance and hierarchies of evolution equations for the moments of the distribution of the magnetization are obtained. In each case, assumptions are spelled out, in order to close the hierarchies. These closure assumptions are tested by extensive numerical studies, that probe the validity of Gaussian or non--Gaussian closure Ans\"atze.