Asymptotic behavior for the 1-D stochastic Landau Lifshitz Bloch equation

Abstract

The stochastic Landau-Lifshitz-Bloch equation describes the phase spins in a ferromagnetic material and has significant role in simulating heat-assisted magnetic recording. In this paper, we consider the deviation of the solution to the 1-D stochastic Landau-Lifshitz-Bloch equation, that is, we give the asymptotic behavior of the trajectory $\frac{u_{\epsilon }-u_0}{\sqrt{\epsilon }\lambda (\epsilon )}$ as $\epsilon \to 0+$, for $\lambda (\epsilon )=\frac{1}{\sqrt{\epsilon }}$ and $1$ respectively. In other words, the large deviation principle and the central limit theorem are established respectively.