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Stochastic dynamics of planar magnetic moments in a three-dimensional environment

Author

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  • Arenas, Zochil González
  • Barci, Daniel G.
  • Moreno, Miguel Vera

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 n-point correlation function, independently of the stochastic calculus used. Using this formalism, we show the equivalence between the cartesian formulation with vectorial noise, and the polar formulation with just one scalar fluctuation term. In particular, we show that, for isotropic fluctuations, the system is represented by an 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.

Suggested Citation

  • Arenas, Zochil González & Barci, Daniel G. & Moreno, Miguel Vera, 2018. "Stochastic dynamics of planar magnetic moments in a three-dimensional environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 98-109.
    • Handle: RePEc:eee:phsmap:v:510:y:2018:i:c:p:98-109
    DOI: 10.1016/j.physa.2018.06.126
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    Cited by:

    1. Silvano, Nathan O. & Barci, Daniel G., 2023. "The role of multiplicative noise in critical dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).

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