Models WDn in the presence of disorder and the coupled models

We have studied the conformal models WD _n^(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 ɛ-expansion in ɛ=1/ p. We have found that the disorder makes to flow the model WD_n^{( p)} to the model WD_n^{( p-1)} without disorder. In the related problem of N coupled regular WD_n^{( p)} models (no disorder), coupled by their energy operators, we find a flow to the fixed point of N decoupled WD_n^{( 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.