The Potts-q random matrix model : loop equations, critical exponents, and rational case

Details The Potts-q random matrix model : loop equations, critical exponents, and rational case The Potts-q random matrix model : loop equations, critical exponents, and rational case

1999-06-17

arxiv.org/abs/hep-th/9906130v1

Phys.Lett.B463:273-279,1999

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, submitted to Phys. Letters B

Scientific paper

10.1016/S0370-2693(99)00925-9

In this article, we study the q-state Potts random matrix models extended to branched polymers, by the equations of motion method. We obtain a set of loop equations valid for any arbitrary value of q. We show that, for q=2-2 \cos {l \over r} \pi (l, r mutually prime integers with l < r), the resolvent satisfies an algebraic equation of degree 2 r -1 if l+r is odd and r-1 if l+r is even. This generalizes the presently-known cases of q=1, 2, 3. We then derive for any 0 \leq q \leq 4 the Potts-q critical exponents and string susceptibility.

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