Critical Behaviour of a Fermionic Random Matrix Model at Large-N

Abstract

We study the large-$N$ limit of adjoint fermion one-matrix models. We find one-cut solutions of the loop equations for the correlators of these models and show that they exhibit third order phase transitions associated with $m$-th order multi-critical points with string susceptibility exponents $\gamma_{\rm str}=-1/m$. We also find critical points which can be interpreted as points of first order phase transitions, and we discuss the implications of this critical behaviour for the topological expansion of these matrix models.