  XY frustrated magnets exhibit an unsual critical behavior: they display
scaling laws accompanied by nonuniversal critical exponents and a negative
anomalous dimension. This suggests that they undergo weak first order phase
transitions. We show that all perturbative approaches that have been used to
investigate XY frustrated magnets fail to reproduce these features. Using a
nonperturbative approach based on the concept of effective average action, we
are able to account for this nonuniversal scaling and to describe qualitatively
and, to some extent, quantitatively the physics of these systems.
