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arXiv · hep-th/9906130

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

B. Eynard·G. Bonnet
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Abstract

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} π(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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B. Eynard, G. Bonnet. 1999-06-17. The Potts-q random matrix model : loop equations, critical exponents, and rational case. https://doi.org/10.1016/s0370-2693(99)00925-9

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