Stochastic dynamics of planar magnetic moments in a three-dimensional environment
arXiv:1802.01027 · doi:10.1016/j.physa.2018.06.126
Abstract
We study the stochastic dynamics of a two-dimensional magnetic moment embedded in a three-dimensional environment, described by means of the stochastic Landau-Lifshitz-Gilbert (sLLG) equation. We define a covariant generalization of this equation, valid in the "generalized Stratonovich discretization prescription". We present a path integral formulation that allows to compute any point correlation function, independently of the stochastic calculus used. Using this formalism, we show the equivalence between the cartesian formulation with vectorial noise, with the polar formulation with just one scalar fluctuation term. In particular, we show that, for isotropic fluctuations, the system is represented by an {\em additive stochastic process}, despite of the multiplicative terms appearing in the original formulation of the sLLG equation, but, for anisotropic fluctuations the noise turns out to be truly multiplicative.
arXiv comment10 pages, no figures, final version accepted in Physica A
References in corpus (19)
- Discovery of intrinsic ferromagnetism in 2D van der Waals crystals
- State-dependent diffusion: thermodynamic consistency and its path integral formulation
- Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation
- Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise
- Nature of Long-Range Order in Stripe-Forming Systems with Long-Range Repulsive Interactions
- Orientational order in two dimensions from competing interactions at different scales
- Dynamical symmetries of Markov processes with multiplicative white noise
- Competing Interactions, the Renormalization Group and the Isotropic-Nematic Phase Transition
- Numerical integration of the stochastic Landau-Lifshitz-Gilbert equation in generic time-discretisation schemes
- Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes
- Rapidly driven nanoparticles: Mean first-passage times and relaxation of the magnetic moment
- Quantum and thermal melting of stripe forming systems with competing long ranged interactions
- Supersymmetric formulation of multiplicative white--noise stochastic processes
- Langevin dynamics for vector variables driven by multiplicative white noise: a functional formalism
- Microscopic approach to orientational order of domain walls
- Distributions of switching times of single-domain particles using a time quantified Monte Carlo method
- Nematic Phase in two-dimensional frustrated systems with power law decaying interactions
- Non-Markovian magnetization dynamics for uniaxial nanomagnets
- Colored-noise magnetization dynamics: from weakly to strongly correlated noise