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

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.

arXiv comment16 pages, 10 figures

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Cited by in corpus (6)

• Multiple phases and meromorphic deformations of unitary matrix models
• Multiple phases in a generalized Gross-Witten-Wadia matrix model
• Phases of unitary matrix models and lattice QCD2
• Conformal Invariance and Phase Transitions: Implications for Stable Black Hole Horizons?
• Fermionic Matrix Models and Bosonization
• On the computation of density and two-point correlation functions of a class of random matrix ensembles