Distribution function of lattice systems of finite dimensions with respect to the number of particles in a large canonical ensemble

One method to identify a phase transition of the first kind is to study the distribution function of a system with respect to the number of particles in a large canonical ensemble, i.e., the probability that the system contains N particles. The presence of multiple extrema in the distribution function attest to the possibility of phase transitions. Recurrence relations which make it possible to calculate the distribution function of systems with respect to the number of particles in a large canonical ensemble have been obtained for one-dimensional lattice systems of finite dimensions.