Critical properties of a continuous family of XY noncollinear magnets

Monte Carlo methods are used to study a family of three dimensional XY frustrated models interpolating continuously between the stacked triangular antiferromagnets and a variant of this model for which a local rigidity constraint is imposed. Our study leads us to conclude that generically weak first order behavior occurs in this family of models in agreement with a recent nonperturbative renormalization group description of frustrated magnets.