Random Bond perturbations of the $O(2)$ vector model

TL;DR

This paper studies how quenched disorder affects the critical $O(2)$ vector model, using conformal perturbation theory and numerical bootstrap data to identify a new fixed point where symmetry is restored.

Contribution

It provides a detailed analysis of disorder effects in the $O(2)$ model, including a novel computation in 3d and insights into anisotropic disorder and symmetry restoration.

Findings

Disorder induces a new fixed point in the $O(2)$ model.

Symmetry broken locally by disorder is restored in the IR.

The study combines conformal perturbation theory with numerical bootstrap data.

Abstract

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.