COUPLED MINIMAL MODELS WITH AND WITHOUT DISORDER

We analyze in this article the critical behavior of M q(1)-state Potts models coupled to N q(2)-state Potts models (q(1), q(2) is an element of [2,...,4]) With and without disorder. The techniques we use are ba sed on perturbed conformal theories. Calculations have been performed at two loops. We already find same interesting situations in the pure case for some peculiar values of M and N with new tricritical points. When adding weak disorder, the results we obtain tend to show that dis order makes the models decouple, Therefore, no relations emerges, at a perturbation level, between for example the disordered q(1) x q(2)-st ate Potts model and the two disordered q(1), q(2)-state Pens models (q (1) not equal q(2)), despite the fact that their central charges are s imilar according to recent numerical investigations. (C) 1998 Elsevier Science B.V.