Investigation of the Potts Model Using Renormalization-Group Techniques

We report the numerical study, using Wilson's $\eta =0\mathrm{}$ approximate renormalization-group recursion formula, of a continuous-spin generalization of the three-component Potts model. Previous numerical studies, based on series expansions of the partition function, have indicated strongly that the model has a phase transition of second order. This is in conflict with Landau theory which predicts that the transition be of first order. We find, in agreement with Landau theory, that our model exhibits a first-order phase transition having finite zero-field spontaneous magnetization at the transition point.