Publication : t99/060

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 $q=2 -2 \cos {l \over r} \pi~(l,r~{\rm ~mutually~prime~ integers~with}~l < r),$ the resolvent satisfies an algebraic equation of degree $2 r -1~{\rm if}~l+r~{\rm odd~and}~r-1~{\rm if}~l+r$ 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.