Renormalization and phase transitions in Potts [fi]/sup 3/-field theory with quadratic and trilinear symmetry breaking

Abstract

Renormalized perturbation theory with generalized minimal subtraction is used as an appropriate renormalization-group procedure for the study of crossover behavior in the continuum version of the p-state Potts model with quadratic and trilinear symmetry breaking, within the representation of Priest and Lubensky, by means of a two-loop-order calculation in d =6-€ dimensions. The boundary between first- and second-order phase transitions is studied for longitudinal and transverse ordering as a function of p. A fixed-point runaway for longitudinal ordering is consistent with a mean-field interpretation of a first-order transition for p >p*, where p* >/2 but not with a secondorder transition for p <P *. Finite and stable fixed points are obtained for transverse ordering, one that follows by crossover from the symmetric fixed point for 2 <P < 13/3, in consistency with the usual mean-field interpretation of a second-order transition for 2 <P < 3.