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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 ⩽ 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 (q1×q2)-state Potts model and the two disordered q1, q2-state Potts models (q1 ≠ q2), though recent numerical investigations have shown that their central charges are approximately similar.