Journal of Statistical Physics, Vol. 81, Nos. 3/4, 1995, p. 647-672.
The collective variables method with a reference system is developed for the case
of the grand canonical ensemble for a multicomponent continuous system. The
method is used to investigate phase transitions in a binary system. For a binary
symmetrical system the relations between microscopic parameters determining
the alternation of gas-liquid and separation phase transitions are found. The
functional of the grand partition function of the symmetrical mixture is
examined in the framework of parameters containing the separation point. The
system is described with two sets of collective variables: p~, a set connected with
the gas-liquid critical point, and ck, a set connected with the separation
phenomenon. The fourfold basic density measure is constructed in ck-variable
phase space which contains the variable c o connected with the order parameter
of the system. It is shown that the problem can be reduced to the 3D Ising
model in an external field.