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

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

2010-01-25

arxiv.org/abs/1001.4355v1

J.Stat.Mech.(2010)P03023

Physics

Mathematical Physics

Scientific paper

10.1088/1742-5468/2010/03/P03023

We present a method to study 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 C1 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 a birth of a cut.

Affiliated with

Also associated with

No associations

Rating

Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Phase transitions in multi-cut matrix models and matched solutions of Whitham hierarchies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-130492