Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework

Julien Tranchida (1) , Pascal Thibaudeau (2) , Stam Nicolis (3)

1 SNL - Sandia National Laboratories [Albuquerque]
2 CEA Le Ripault - CEA Le Ripault
3 IDP - Institut Denis Poisson

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 Ansätze.

Domains: Chaotic Dynamics [nlin.CD]; Statistical Mechanics [cond-mat.stat-mech]; Computational Physics [physics.comp-ph]

Julien Tranchida, Pascal Thibaudeau, Stam Nicolis. Hierarchies of Landau-Lifshitz-Bloch equations for nanomagnets: A functional integral framework. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2018, 98 (4), pp.042101. ⟨10.1103/PhysRevE.98.042101⟩. ⟨cea-01885680⟩