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An n-component generalization of the continuous Potts model is studied both in the ordered and in the disordered phase by using Wilson's epsilon and 1/n expansions around the Heisenberg fixed point. The results indicate that the transition is always of first order for d=3. For the case of a small first-order transition, exponents are derived in the critical region around the transition temperature and the crossover to the isotropic behaviour is discussed. A close relation to equivalent results for a model with quartic anisotropy is also manifested.
R.H. Oppermann (Tue,) studied this question.