Fluctuating local field method for the disordered Ising model

Abstract: We present a method for computing thermal properties of classical spin clusters with arbitrarily chosen interactions between spins. For such systems, instability channels are \textit{a priori} not known. The method is based on the Fluctuating Local Field (FLF) approach, the effective description of the system with a nonlinear and fluctuating field, and achieves substantial improvements over mean-field theory. We show that two fluctuating modes are sufficient for numerically accurate solution of systems consisting of two dozen spins, while for larger systems it is needed to account for a larger number of fluctuating modes for a full quantitative agreement with the exact solution.