Coupled Minimal Models with and without Disorder

We analyse in this article the critical behavior of $M$ $q_1$-state Potts models coupled to $N$ $q_2$-state Potts models ($q_1,q_2\in [2..4]$) with and without disorder. The technics we use are based on perturbed conformal theories. Calculations have been performed at two loops. We already find some 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 disorder makes the models decouple. Therefore, no relations emerges, at a perturbation level, between for example the disordered $q_1\times q_2$-state Potts model and the two disordered $q_1,q_2$-state Potts models ($q_1\ne q_2$), despite their central charges are similar according to recent numerical investigations.