For pt.I, see ibid., vol.22, p.4971 (1989). The fluctuations in the ordered phase around the mean-field solution are incorporated in a renormalization group approach and it is found that for a small range of the parameters they restore scaling close to the upper critical dimension. For the 3-state case it appears that fluctuations destroy the stability of the solution and cause the system to undergo a first-order phase transition. Non-universal fluctuation corrections to the equation of state above six dimensions are obtained.
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Gabriel Cwilich (1990) studied this question.
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