A Curie-Weiss theory of the continuum Widom-Rowlinson model

A version of the continuum Widom-Rowlinson model is introduced and studied. It is a two-component gas of point particles placed in Rd in which like particles do not interact and unlike particles contained in a given vessel of volume V repel each other with intensity a/V. This model is thermodynamically equivalent to a one-component gas with multi-particle interaction. For both models, a rigorous theory of a phase transition is presented and the ways of its construction in the framework of the grand canonical formalism are outlined.