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 $\frac{u_\varepsilon-u_0}{\sqrt{\varepsilon}\lambda(\varepsilon)}$ as $\varepsilon\rightarrow 0+$, for $\lambda(\varepsilon)=\frac{1}{\sqrt{\varepsilon}}$ and $1$ respectively. In other words, the large deviation principle and the central limit theorem are established respectively.