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

Fuente: arXiv
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Main Authors: Cava, Giulia, Giuliani, Alessandro, Greenblatt, Rafael Leon
Format: Preprint
Published: 2024
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author Cava, Giulia
Giuliani, Alessandro
Greenblatt, Rafael Leon
author_facet Cava, Giulia
Giuliani, Alessandro
Greenblatt, Rafael Leon
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2408_12923
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The scaling limit of boundary spin correlations in non-integrable Ising models
Cava, Giulia
Giuliani, Alessandro
Greenblatt, Rafael Leon
Mathematical Physics
Statistical Mechanics
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.
title The scaling limit of boundary spin correlations in non-integrable Ising models
topic Mathematical Physics
Statistical Mechanics
url https://arxiv.org/abs/2408.12923