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

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.

50 pages, 11 figures, 3 tables v2 minor typos fixed, references updated, matches journal

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Cited by in corpus (35)

• The critical O(N) CFT: Methods and conformal data
• Spin Impurities, Wilson Lines and Semiclassics
• Bootstrapping line defects with $O(2)$ global symmetry
• Broken global symmetries and defect conformal manifolds
• Notes on a Surface Defect in the $O(N)$ Model
• A Scaling Limit for Line and Surface Defects
• Analytic bootstrap for the localized magnetic field
• A dispersion relation for defect CFT
• The $g$-function and Defect Changing Operators from Wavefunction Overlap on a Fuzzy Sphere
• Phases of Wilson Lines in Conformal Field Theories
• Line Defect RG Flows in the $\epsilon$ Expansion
• Studying the 3d Ising surface CFTs on the fuzzy sphere
• Integrated correlators from integrability: Maldacena-Wilson line in $\mathcal{N}=4$ SYM
• The epsilon expansion of the O$(N)$ model with line defect from conformal field theory
• Defects in scalar field theories, RG flows and Dimensional Disentangling
• Solving Conformal Defects in 3D Conformal Field Theory using Fuzzy Sphere Regularization
• RG flows on two-dimensional spherical defects
• Comments on epsilon expansion of the O$(N)$ model with boundary
• Non-Perturbative Defects in Tensor Models from Melonic Trees
• Renormalization group flows in AdS and the bootstrap program
• RG Flows and Stability in Defect Field Theories
• Analytic bootstrap for magnetic impurities
• Polyakov blocks for the 1D CFT mixed correlator bootstrap
• Defects, Rigid Holography and $C$-theorems
• Conformal line defects at finite temperature
• Defect Localized Entropy: Renormalization Group and Holography
• Wilson loops in Large Symmetric Representations through a Double-Scaling Limit
• Critical crossover phenomena driven by symmetry-breaking defects at quantum transitions
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• Probing Defects with Quantum Simulator Snapshots
• A Fuzzy Sphere Journey in Critical Phenomena
• The $O(N)$ Free-Scalar and Wilson-Fisher Conformal Field Theories on the Fuzzy Sphere
• Fine Spectrum from Crude Analytic Bootstrap
• Casimir effect in critical $\mathrm{O}(N)$ models from non-equilibrium Monte Carlo simulations
• Finite-coupling spectrum of O(N) model in AdS