Critical behavior of coupled q-state Potts models under weak disorder

We investigate the effects of weak disorder on different coupled q-state Potts models with q less than or equal to 4 using two-loop renormalisation group equations. This study presents new examples of first-order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relation emerges, at a perturbation level, between the disordered (q(1) x q(2))-state Potts model and the two disordered q(1), q(2)-state Potts models (q(1) not equal q(2)), though recent numerical investigations have shown that, their central charges are approximately similar.