Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1995-02-22
Commun.Math.Phys. 177 (1996) 451-468
Physics
High Energy Physics
High Energy Physics - Theory
22 pages, harvmac.tex, pictex.tex. All diagrams written directly into the text in Pictex commands. (Two minor math typos corre
Scientific paper
10.1007/BF02101902
We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the large N limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the large $N$ limit of the Itzykson-Zuber formula. We illustrate and check our methods by analyzing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphs possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problem of phase transitions from random to flat lattices.
Kazakov Vladimir A.
Staudacher Matthias
Wynter Thomas
No associations
LandOfFree
Character Expansion Methods for Matrix Models of Dually Weighted Graphs 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 Character Expansion Methods for Matrix Models of Dually Weighted Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Character Expansion Methods for Matrix Models of Dually Weighted Graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-30378