  An analog of the continuum Widom-Rowlinson model is introduced and studied.
Its two-component version is a gas of point particles of types 0 and 1 placed
in $\mathds{R}^d$, in which like particles do not interact and unlike particles
contained in a vessel of volume $V$ repel each other with intensity $a/V$. The
one-component version is a gas of particles with multi-particle interactions of
Curie-Weiss type. Its thermodynamic behavior is obtained by integrating out the
coordinates of one of the components of the two-component version. In the grand
canonical setting, a rigorous theory of phase transitions in this model is
developed and discussed. In particular, for both versions thermodynamic phases
and phase diagrams are explicitly constructed and the equations of state are
obtained and analyzed.
