PHASE-TRANSITIONS WITH O(N) SYMMETRY BROKEN DOWN TO O(N-P)

We define the Stiefel models (a generalization of the Heisenberg model), and investigate their phase transitions. These models are built so as to have a phase transition with an O(n) symmetry broken down to O(n - p). The group-theoretical properties of the models are reviewed. The mean field equation is solved. As the usual perturbative renormalization group fails, we use the local potential approximation of the renormalization group in order to obtain the critical exponents in three dimensions. The most interesting model physically possesses an almost second-order phase transition, with the exponent nu = 0.63.