RT Journal Article
T1 Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies
A1 Álvarez Galindo, Gabriel
A1 Martínez Alonso, Luis
A1 Medina Reus, Elena
AB 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.
PB IOP Publishing
SN 1742-5468
YR 2010
FD 2010-03
LK https://hdl.handle.net/20.500.14352/43721
UL https://hdl.handle.net/20.500.14352/43721
LA eng
NO �© 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.
NO Universidad Complutense
NO Comisión Interministerial de Ciencia y Tecnología
NO ESF programme MISGAM.
DS Docta Complutense
RD 6 abr 2025