  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. 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 KPZ values associated with
Ising spins, and with the exact two-matrix model solution of the random Ising
model, introduced previously to describe the effects of fluctuating geometries.
