Perturbative approach to the critical behaviour of two-matrix models in the limit N -> infinity

Abstract

We construct representations of the Heisenberg algebra by pushing the perturbation expansion to high orders. If the multiplication operators $B_{1,2}$ tend to differential operators of order $l_{2,1}$, respectively, the singularity is characterized by $(l_1,l_2)$. Let $l_1\ge l_2$. Then the two cases A : ``$l_2$ does not divide $l_1$'' and B : ``$l_2$ divides $l_1$'' need a different treatment. The universality classes are labelled $[p,q]$ where $[p,q]$=[$l_1$,$l_2$] in case A and $[p,q]$=[$l_1+1$,$l_2$] in case B.

23 pages, LateX

References in corpus (2)

• 2D Gravity and Random Matrices
• Rational Theories of 2D Gravity from the Two-Matrix Model

Cited by in corpus (2)

• The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit
• On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3