Perturbative continued-fraction method for weakly interacting Brownian spins and dipoles

The continued-fraction method was developed systematically by Risken and co-workers to solve problems of arbitrary fluctuations in nonlinear systems. However, this efficient technique is limited to problems with a few variables, which in practice means systems of noninteracting entities (particles, spins, etc.) We illustrate how to extend the continued-fraction method to weakly coupled systems with the problem of relaxation in classical spins.