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

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 $varepsilonrightarrow 0+$, 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.