Evaluating the partition function for systems with long range interactions
arXiv:cond-mat/9902280 · doi:10.1016/S0375-9601(00)00148-1
Abstract
We express the partition function for an equilibrium system of interacting particles in the canonical ensemble as a functional integration over the particles' density field. We outline a method to evaluate the partition function by expanding around a saddle point. The saddle point is shown to be the solution of the equivalent mean-field theory. Leading corrections to the mean-field theory takes the form of a Gaussian integral.