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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Official URL: http://prd.aps.org/abstract/PRD/v42/i12/p4105_1

Related URL: http://dx.doi.org/10.1103/PhysRevD.42.4105

## Abstract

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 φ^{6} 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 R_{r}, 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 R_{n} 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 φ^{8} potential, and a k=1-type nonperturbative solution from the three-band phase in the φ^{6} 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.

Item Type: | Article |
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Source: | Copyright of this article belongs to American Physical Society. |

ID Code: | 12765 |

Deposited On: | 11 Nov 2010 09:00 |

Last Modified: | 17 Feb 2011 08:36 |

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