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

@article{Eynard1999ThePR,
title={The Potts-q random matrix model: loop equations, critical exponents, and rational case},
author={Bertrand Eynard and G. Bonnet},
journal={Physics Letters B},
year={1999},
volume={463},
pages={273-279}
}
• Published 1999
• Physics
• Physics Letters B
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 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≤ q ≤4 the Potts- q… Expand
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