The scaling limit of boundary spin correlations in non-integrable Ising models

We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the half-plane. We prove that the leading order long-distance behavior of...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Cava, Giulia, Giuliani, Alessandro, Rafael Leon Greenblatt
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.08.2024
Subjects
Correlation
Half planes
Ising model
Multiscale analysis
Online AccessGet full text

Cover

More Information
Summary:We consider a class of non-integrable 2D Ising models obtained by perturbing the nearest-neighbor model via a weak, finite range potential which preserves translation and spin-flip symmetry, and we study its critical theory in the half-plane. We prove that the leading order long-distance behavior of the correlation functions for spins on the boundary is the same as for the nearest-neighbor model, up to an analytic multiplicative renormalization constant. In particular, the scaling limit is the Pfaffian of an explicit matrix. The proof is based on an exact representation of the generating function of correlations in terms of a Grassmann integral and on a multiscale analysis thereof, generalizing previous results to include observables located on the boundary.
ISSN:2331-8422