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English

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

Published inAnnales de l'I.H.P. Probabilités et statistiques, vol. 60, no. 1, p. 167-207
Publication date2024-03-05
Abstract

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.

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Keywords
  • Ising model
  • Ornstein-Zernike asymptotics
  • Long-range interactions
  • Correlation length
  • Analyticity
  • Coarse-graining
  • Polymers
Citation (ISO format)
AOUN, Yacine, OTT, Sébastien, VELENIK, Yvan. Ornstein-Zernike behavior for Ising models with infinite-range interactions. In: Annales de l’I.H.P. Probabilités et statistiques, 2024, vol. 60, n° 1, p. 167–207. doi: 10.1214/22-AIHP1345
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Article (Published version)
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Identifiers
ISSN of the journal0246-0203
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