  We investigate the impact of quenched disorder in the critical $O(2)$ vector
model. We first review, in the modern language of Conformal Perturbation
Theory, the random temperature perturbation in $4-\epsilon$. Then, we present a
direct computation in $3d$. The pure CFT is now strongly interacting, and its
CFT data are determined in recent numerical bootstrap studies. We then explore
the anisotropic disorder associated with the lowest-dimension charge-$2$
scalar, which is relevant in $3d$. This perturbation breaks locally $O(2)$.
However, the symmetry is restored in the IR in a weakly coupled new fixed
point.
