  In multitype lattice gas models with hard-core interaction of
Widom--Rowlinson type, there is a competition between the entropy due to the
large number of types, and the positional energy and geometry resulting from
the exclusion rule and the activity of particles. We investigate this
phenomenon in four different models on the square lattice: the multitype
Widom-Rowlinson model with diamond-shaped resp. square-shaped exclusion between
unlike particles, a Widom-Rowlinson model with additional molecular exclusion,
and a continuous-spin Widom-Rowlinson model. In each case we show that this
competition leads to a first-order phase transition at some critical value of
the activity, but the number and character of phases depend on the geometry of
the model. Our technique is based on reflection positivity and the chessboard
estimate.
