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

TL;DR

This paper studies the effects of a localized magnetic field on the critical $O(N)$ model, predicting the resulting defect conformal field theory data using epsilon expansion and large $N$ techniques, with results compatible with simulations.

Contribution

It introduces a novel analysis of the defect RG flow in the $O(N)$ model with a localized magnetic field, employing new saddle point methods and recent AdS loop diagram progress.

Findings

Prediction of defect CFT data in epsilon expansion and large N limit.

Identification of a stable nontrivial defect CFT with $g<1$.

Compatibility with Monte Carlo simulation results.

Abstract

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 $g<1$. We obtain several predictions for the corresponding DCFT data in the epsilon expansion and in the large $N$ limit. The analysis of the large $N$ limit involves a new saddle point and, remarkably, the study of fluctuations around it is enabled by recent progress in AdS loop diagrams. Our results are compatible with results from Monte Carlo simulations and we make several predictions that can be tested in the future.