Abstract
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: ρk, a set connected with the gas-liquid critical point, andck, a set connected with the separation phenomenon. The fourfold basic density measure is constructed inck-variable phase space which contains the variablecv 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.
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