Brownian dynamics approach to interacting magnetic moments

The question of how to introduce thermal fluctuations in the equation of motion of a magnetic system is addressed. Using the approach of the fluctuation-dissipation theorem we calculate the properties of the noise for both, the fluctuating field and the additive fluctuating torque (force) representation. In contrast to earlier calculations we consider the general case of a system of interacting magnetic moments. We show that the interactions do not result in any correlations of thermal fluctuations in the field representation and that the same widely used formula can be used in the most general case. We further prove that close to the equilibrium where the fluctuation-dissipation theorem is valid, both, field and additive torque (force) representations coincide, being different far away from it. We also show that the uncorrelated character of the noise is due to the form of the Landau-Lifshitz (or Gilbert) damping and under different damping formalisms, the normal mode analysis is proper