MULTI-SPIN SYSTEMS ON A RANDOMLY TRIANGULATED SURFACE

We consider a class of spin systems on randomly triangulated surfaces as discrete approximations of conformal matter fields coupled to 2d gravity. On the basis of certain universality assumptions we argue that at critical points with diverging string susceptibility (c greater than or equal to 1) the model either exhibits mean field behaviour or it can effectively be described by a conformal matter system with central charge (c) over bar less than or equal to 1 coupled to 2d gravity. As a particular consequence we conclude in the unitary case that the string susceptibility exponent gamma is limited to possible values of the form 1/n, n = 2, 3, 4,..., where n = 2 corresponds to mean field behaviour.