Randomly coupled minimal models

Using 1-loop renormalisation group equations, we analyze the effect of randomness on multi-critical unitary minimal conformal models. We study the case of two randomly coupled $M_p$ models and found that they flow in two decoupled $M_{p-1}$ models, in the infra-red limit. This result is then extend to the case with $M$ randomly coupled $M_p$ models, which will flow toward $M$ decoupled $M_{p-1}$.