Crossover exponents for the potts model with quadratic symmetry breaking

Abstract

The effect of quadratic symmetry breaking (QSB) on two representations for the Potts vectors in a continuum-field model are studied to two-loop order in renormalized perturbation theory in d=6-E dimensions, in extension of an earlier group-theoretical analysis by Wallace and Young. The explicit dependence of the crossover exponent ф that corresponds to QSB that destroys the equivalence between pairs of Potts vectors is obtained as a function of d and n for the p-state model with p = n + 1. It is shown that this exponent follows from the calculation of vertex functions in a representation dueto Wallace and Young, whereas a second crossover exponent ф, that can be identified with the criticai exponent β, and which corresponds to QSB that favors a single Potts vector against the others, follows from a calculation using the representation of the Potts vectors due to Priest and Lubensky.