Ornstein-Zernike behavior for Ising models with infinite-range interactions

Fuente: arXiv
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Main Authors: Aoun, Yacine, Ott, Sébastien, Velenik, Yvan
Format: Preprint
Published: 2021
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author Aoun, Yacine
Ott, Sébastien
Velenik, Yvan
author_facet Aoun, Yacine
Ott, Sébastien
Velenik, Yvan
contents We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the interaction. The main contribution of this work is that the interactions are not assumed to be of finite range. To the best of our knowledge, this is the first proof of OZ asymptotics for a nontrivial model with infinite-range interactions. Our results actually apply to the Green function of a large class of "self-repulsive in average" models, including a natural family of self-repulsive polymer models that contains, in particular, the self-avoiding walk, the Domb-Joyce model and the killed random walk. We aimed at a pedagogical and self-contained presentation.
format Preprint
id arxiv_https___arxiv_org_abs_2112_13057
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle Ornstein-Zernike behavior for Ising models with infinite-range interactions
Aoun, Yacine
Ott, Sébastien
Velenik, Yvan
Mathematical Physics
Statistical Mechanics
Probability
We prove Ornstein-Zernike behavior for the large-distance asymptotics of the two-point function of the Ising model above the critical temperature under essentially optimal assumptions on the interaction. The main contribution of this work is that the interactions are not assumed to be of finite range. To the best of our knowledge, this is the first proof of OZ asymptotics for a nontrivial model with infinite-range interactions. Our results actually apply to the Green function of a large class of "self-repulsive in average" models, including a natural family of self-repulsive polymer models that contains, in particular, the self-avoiding walk, the Domb-Joyce model and the killed random walk. We aimed at a pedagogical and self-contained presentation.
title Ornstein-Zernike behavior for Ising models with infinite-range interactions
topic Mathematical Physics
Statistical Mechanics
Probability
url https://arxiv.org/abs/2112.13057