Models WDn in the presence of disorder and the coupled models

We have studied the conformal models WDn(p), n=3,4,5,..., in the presence of disorder which couples to the energy operator of the model. In the limit of p>>1, where p is the corresponding minimal model index, the problem could be analyzed by means of the perturbative renormalization group, with ε-expansion in ε=1/p. We have found that the disorder makes to flow the model WDn(p) to the model WDn(p-1) without disorder. In the related problem of N coupled regular WDn(p) models (no disorder), coupled by their energy operators, we find a flow to the fixed point of N decoupled WDn(p-1). But in addition we find in this case two new fixed points which could be reached by a fine tuning of the initial values of the couplings. The corresponding critical theories realize the permutational symmetry in a nontrivial way, like this is known to be the case for coupled Potts models, and they could not be identified with the presently known conformal models