Random Ising spins in two dimensions: a flat space realization of the KPZ exponents

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.