Wong–Zakai approximations for the stochastic Landau–Lifshitz–Bloch equations

Abstract

The stochastic Landau–Lifshitz–Bloch equation describes the evolution of spins in ferromagnetic materials for temperatures both below and above the Curie temperature. We consider both exchange and anisotropy energy in dimensions 1 and 2. The equation is transformed into a non-linear partial differential equation with random coefficients, which has a pathwise unique solution. This solution depends continuously on the considered Wiener process. We transform back to the original equation to conclude that the solution to the original equation depends continuously on the Wiener process considered.