  Athermal lattice gases of particles with first neighbor exclusion have been
studied for a long time as simple models exhibiting a fluid-solid transition.
At low concentration the particles occupy randomly both sublattices, but as the
concentration is increased one of the sublattices is occupied preferentially.
Here we study a mixed lattice gas with excluded volume interactions only in the
grand-canonical formalism with two kinds of particles: small ones, which occupy
a single lattice site and large ones, which occupy one site and its first
neighbors. We solve the model on a Bethe lattice of arbitrary coordination
number $q$. In the parameter space defined by the activities of both particles.
At low values of the activity of small particles ($z_1$) we find a continuous
transition from the fluid to the solid phase as the activity of large particles
($z_2$) is increased. At higher values of $z_1$ the transition becomes
discontinuous, both regimes are separated by a tricritical point. The critical
line has a negative slope at $z_1=0$ and displays a minimum before reaching the
tricritical point, so that a reentrant behavior is observed for constant values
of $z_2$ in the region of low density of small particles. The isobaric curves
of the total density of particles as a function of $z_1$ (or $z_2$) show a
minimum in the fluid phase.
