Communications in Mathematical Physics

, Volume 177, Issue 2, pp 451–468 | Cite as

Character expansion methods for matrix models of dually weighted graphs

  • Vladimir A. Kazakov
  • Matthias Staudacher
  • Thomas Wynter


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 largeN 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 largeN limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphys possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating the equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problems of phase transitions from random to flat lattices. January 1995


Phase Transition Coordination Number External Field Matrix Model Planar Graphys 
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Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Vladimir A. Kazakov
    • 1
  • Matthias Staudacher
    • 1
  • Thomas Wynter
    • 1
  1. 1.Laboratoire de Physique Théorique de lÉcole Normale SupérieureUniversité de Paris SudParis Cedex 05France

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