MULTIPLE ISING SPINS COUPLED TO 2D QUANTUM-GRAVITY

We study a model in which p independent Ising spins are coupled to 2d quantum gravity (in the form of dynamical planar phi3 graphs). Consideration is given to the p --> infinity limit in which the partition function becomes dominated by certain graphs; we identify most of these graphs. A truncated model is solved exactly providing information about the behaviour of the full model in the limit beta --> 0. Finally, we derive a bound for the critical value of the coupling constant, beta(c) and examine the magnetization transition in the limit p --> 0.