The continuum generalization of the p-state Potts model is analyzed in the ordered phase. Renormalization-group iterations in d=4-ε dimensions are followed by an elimination of the transverse modes and a mapping onto an effective Ising model. This model is then used to show that the transition is first order for p>pc(d) and continuous for p<pc(d). We find that pc(d)=2 for $d>4$ and pc(4-ε)=2+ε+O(ε²).
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Aharony et al. (1981) studied this question.
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