RT journal article
T1 Phase space and phase transitions in the Penner matrix model with negative coupling constant
A1 Alvarez, Gabriel
A1 Martínez Alonso, Luis
A1 Medina Reus, Elena Blanca
A2 Matemáticas
AB The partition function of the Penner matrix model for both positive andnegative values of the coupling constant can be explicitly written in terms of the BarnesG function. In this paper we show that for negative values of the coupling constant thispartition function can also be represented as the product of an holomorphic matrixintegral by a nontrivial oscillatory function of n. We show that the planar limit ofthe free energy with ’t Hooft sequences does not exist. Therefore we use a certainmodification that uses Kuijlaars-McLaughlin sequences instead of ’t Hooft sequencesand leads to a well-defined planar free energy and to an associated two-dimensionalphase space. We describe the different configurations of complex saddle points of theholomorphic 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, eigenvaluetunneling, and Bose condensation.
PB Institute of Physics Publishing
SN 1751-8121
YR 2017
FD 2017
LK http://hdl.handle.net/10498/35449
UL http://hdl.handle.net/10498/35449
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026