  A model describing Ising spins with short range interactions moving randomly
in a plane is considered. In the presence of a hard core repulsion, which
prevents the Ising spins from overlapping, the model is analogous to a
dynamically triangulated Ising model with spins constrained to move on a flat
surface. It is found that as a function of coupling strength and hard core
repulsion the model exhibits multicritical behavior, with first and second
order transition lines terminating at a tricritical point. The thermal and
magnetic exponents computed at the tricritical point are consistent with the
exact two-matrix model solution of the random Ising model, introduced
previously to describe the effects of fluctuating geometries.
