GENERALIZED PENNER MODELS AND MULTICRITICAL BEHAVIOR

In this paper, we are interested in the critical behavior of generalized Penner models at t approximately -1 + mu/N where the topological expansion for the free energy develops logarithmic singularities: GAMMA approximately -(chi(0)mu(2)ln-mu + chi(1)ln-mu + ...). We demonstrate that these criticalities can best be characterized by the fact that the large-N generating function becomes meromorphic with a single pole term of unit residue, F(z) --> 1/(z-a), where a is the location of the "sink." For a one-band eigenvalue distribution, we identify multicritical potentials; we find that none of these can be associated with the c = 1 string compactified at an integral multiple of the self-dual radius. We also give an exact solution to the Gaussian Penner model and explicitly demonstrate that, at criticality, this solution does not correspond to a c = 1 string compactified at twice the self-dual radius.