Deformed Cauchy random matrix ensembles and large $N$ phase transitions

TL;DR

This paper investigates a hermitian matrix model with a logarithmic potential, revealing a third-order phase transition at a critical coupling, which advances understanding of large N phase behavior in such ensembles.

Contribution

It introduces a new matrix model with a Penner-like term and analyzes its phase transition behavior as the coupling varies.

Findings

Potential develops a double well beyond critical coupling

System exhibits a third-order phase transition at a specific coupling

Model provides insights into large N phase transitions in deformed ensembles

Abstract

We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large $N$ third-order phase transition.