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

In this article, we study the cl-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 - 2cos l/r pi (l, r mutually prime integers with l < r), the resolvent sat isfies 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 less than or equal to q less than or equal to 4 the P otts-q critical exponents and string susceptibility. (C) 1999 Elsevier Scie nce B.V. All rights reserved.