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

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 2r− 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 critical exponents and string susceptibility. [email protected]