23-01E

In this paper, we will systematically present the method of collective variables with a reference system for a classical many-particle interacting system in the grand canonical ensemble. The emphasis will be placed on the details of calculations. In particular, the usage of total correlation functions defined for the grand canonical ensemble allows us to investigate very accurately the cumulants of the grand partition function for the reference system. It is shown that any cumulant M_n can be expressed as a product of three components: the average particle number within the reference system, a Kronecker’s symbol for n wave vectors, and the n-particle structure factor. The functional expression for the grand partition function is derived, with all coefficients explicitly defined. The coordinates of the critical point are computed in the mean field approximation.