Absence of the partially ordered phase in theq-state models: I. Renormalization group approach

We investigate the q-state models called (N α , N β ) model using an infinitesimal Migdal-Kadanoff renormalization-group method. We distinguish two cases namely the isotropic model and the anisotropic model. The first one presents a critical value of q, q c such that for q q c the partially ordered phase disappears then the model exhibits only phase transition between ferromagnetic phase and disordered one. The phase diagrams in the second case are qualitatively similar to one obtained for Z(6) model for all values of q