Is the antiferromagnetic RP^(2) model in four dimensions trivial?

Abstract

We study the antiferromagnetic RP^(2) model in four dimensions. We find a second order transition with two order parameters, one ferromagnetic and the other antiferromagnetic. The antiferromagnetic sector has mean- field critical exponents and a renormalized coupling which goes to zero in the continuum limit. The exponents of the ferromagnetic channel are not the mean-field ones, but the difference can be interpreted as logarithmic corrections. We perform a detailed analysis of these corrections and conclude the triviality of the continuum limit of this model.