ϵ expansion for the free energy of the continuous three-state Potts model: evidence for a first-order transition

Low-order terms in an epsilon expansion for the free energy of the continuous three-state Potts model are displayed. The free energy has a scaling form and predicts a first-order transition to the order state. Two universal ratios are calculated to first order in epsilon from the expression. The results of this analysis are in good agreement with corresponding results of previous renormalization group analyses of the continuous Potts model.