Models WD_{n} in the presence of disorder and the coupled models

Abstract

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 $epsilon$-expansion in $\epsilon$=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 non-trivial 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.