Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies



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Álvarez Galindo, Gabriel and Martínez Alonso, Luis and Medina Reus, Elena (2010) Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies. Journal of Statistical Mechanics: Theory and Experiment . ISSN 1742-5468

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We present a method for studying phase transitions in the large N limit of matrix models using matched solutions of Whitham hierarchies. The endpoints of the eigenvalue spectrum as functions of the temperature are characterized both as solutions of hodograph equations and as solutions of a system of ordinary differential equations. In particular we show that the free energy of the matrix model is the quasiclassical tau-function of the associated hierarchy, and that critical processes in which the number of cuts changes in one unit are third-order phase transitions described by C(1) matched solutions of Whitham hierarchies. The method is illustrated with the Bleher-Eynard model for the merging of two cuts. We show that this model involves also the birth of a cut.

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�© 2010 IOP Publishing Ltd and SISSA. The financial support of the Universidad Complutense under project GR58/08-910556, that of the Comision Interministerial de Ciencia y Tecnologia under projects FIS2008-00200 and FIS2008-00209, and that of the ESF programme MISGAM are gratefully acknowledged.

Uncontrolled Keywords:Korteweg-Devries Equation, Small Dispersion Limit, Linear Overdetermined Systems, Poisson-Darboux Type, Double Scaling Limit, Classical Integrability, Classical Phase Transitions (Theory), Random Matrix Theory and Extensions
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:20592
Deposited On:05 Apr 2013 10:47
Last Modified:31 Dec 2020 00:01

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