$\mathrm{XY}$ frustrated magnets exhibit an unusual 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 $\mathrm{XY}$ 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.

• Received 5 December 2002

DOI:https://doi.org/10.1103/PhysRevB.67.134422