Phase space and phase transitions in the Penner matrix model with negative coupling constant



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Álvarez Galindo, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena (2017) Phase space and phase transitions in the Penner matrix model with negative coupling constant. Journal of physics A: Mathematical and theoretical, 50 (12). ISSN 1751-8113

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The partition function of the Penner matrix model for both positive and negative values of the coupling constant can be explicitly written in terms of the Barnes G function. In this paper we show that for negative values of the coupling constant this partition function can also be represented as the product of an holomorphic matrix integral by a nontrivial oscillatory function of n. We show that the planar limit of the free energy with 't Hooft sequences does not exist. Therefore we use a certain modification that uses Kuijlaars-McLaughlin sequences instead of 't Hooft sequences and leads to a well-defined planar free energy and to an associated two-dimensional phase space. We describe the different configurations of complex saddle points of the holomorphic matrix integral both to the left and to the right of the critical point, and interpret the phase transitions in terms of processes of gap closing, eigenvalue tunneling, and Bose condensation.

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©IOP Publishing Ltd.
We thank Prof. A. Martínez Finkelshtein for calling our attention to many nice results on zero asymptotics of Laguerre and Jacobi polynomials. The financial support of the Spanish Ministerio de Economía y Competitividad under Project No. FIS2015-63966-P is gratefully acknowledged.

Uncontrolled Keywords:Laguerre-polynomials; Gauge-theories; String theory; 2d Gravity; Parameters; Behavior
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:43005
Deposited On:30 May 2017 18:41
Last Modified:10 Dec 2018 15:09

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