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

TL;DR

This paper investigates the large-N behavior of fermionic one-matrix models, revealing phase transitions and critical points that influence their topological expansion, with implications for understanding their critical phenomena.

Contribution

It presents the first analysis of phase transitions in fermionic matrix models, identifying multi-critical points and their associated string susceptibility exponents.

Findings

Existence of one-cut solutions for the loop equations.

Identification of third order phase transitions with multi-critical points.

Discovery of critical points resembling first order phase transitions.

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.