Multiband structure and critical behavior of matrix models

Demeterfi, Kresimir ; Deo, Nivedita ; Jain, Sanjay ; Tan, Chung I. (1990) Multiband structure and critical behavior of matrix models Physical Review D, 42 (12). pp. 4105-4122. ISSN 0556-2821

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We discuss, perturbatively and nonperturbatively, the multiband phase structure that arises in Hermitian one-matrix models with potentials having several local minima. The tree-level phase diagram for the φ6 potential including critical exponents at the phase boundaries is presented. The multiband structure is then studied from the viewpoint of the orthogonal polynomial recursion coefficients Rr, using the operator formalism to relate them to the large-N limit of the generating function F(z)=(1/N)<tr1/(z-φ)>. We show how a periodicity structure in the sequence of the Rn coefficients naturally leads to multiband structure, and in particular, provide an explicit example of a three-band phase. Numerical evidence for the periodicity structure among the recursion coefficients is given. We then present examples where we identify the double-scaling limit from a multiband phase. In particular, a k=2-type multicritical nonperturbative solution from the two-band phase in the φ8 potential, and a k=1-type nonperturbative solution from the three-band phase in the φ6 potential is found. Both solutions are described by differential equations related to the modified Korteweg-de Vries hierarchy. Finally, we comment on the other phases that coexist with the k=2 pure gravity solution.

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Source:Copyright of this article belongs to American Physical Society.
ID Code:12765
Deposited On:11 Nov 2010 09:00
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