  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.
