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A model describing Ising spins with short range interactions moving randomlyin a plane is considered. In the presence of a hard core repulsion, whichprevents the Ising spins from overlapping, the model is analogous to adynamically triangulated Ising model with spins constrained to move on a flatsurface. As a function of coupling strength and hard core repulsion the modelexhibits multicritical behavior, with first and second order transition linesterminating at a tricritical point. The thermal and magnetic exponents computedat the tricritical point are consistent with the KPZ values associated withIsing spins, and with the exact two-matrix model solution of the random Isingmodel, introduced previously to describe the effects of fluctuating geometries.Comment: RevTeX 3.0, 17 pages + 15 postscript figures available upon request,  CERN-TH-7355/9

Random Ising spins in two dimensions: A flat space realization of the Knizhnik-Polyakov-Zamolodchikov exponents