Localized magnetic field in the $O(N)$ model

Understand

We consider the critical $O(N)$ model in the presence of an external magnetic field localized in space.

• This setup can potentially be realized in quantum simulators and in some liquid mixtures.
• The external field can be understood as a relevant perturbation of the trivial line defect, and thus triggers a defect Renormalization Group (RG) flow.
• In agreement with the $g$-theorem, the external localized field leads at long distances to a stable nontrivial defect CFT (DCFT) with $g<1$.