First- and second-order transitions in the Potts model near four dimensions

The continuum generalization of the p-state Potts model is analyzed in the ordered phase. Renormalization-group iterations in d=4- 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-)=2+O(2).