Asymptotics of correlations in the Ising model: a brief survey

Ott, Sébastien; Velenik, Yvan

Scientific article

English

Asymptotics of correlations in the Ising model: a brief survey

ContributorsOtt, Sébastien; Velenik, Yvan

Published inPanoramas et synthèses - Société mathématique de France, vol. 59, p. 157-184

Publication date2023

First online date2023

Abstract

We present a brief survey of rigorous results on the asymptotic behavior of correlations between two local functions as the distance between their support diverges, concentrating on the Ising model on Z^d with finite-range ferromagnetic interactions.

Keywords

Ising model
Ornstein-Zernike asymptotics
Decay of correlations
Power-law corrections
Mixing
Analyticity
Ursell functions

Affiliation entities

Faculté des sciences / Section de mathématiques

Citation (ISO format)

OTT, Sébastien, VELENIK, Yvan. Asymptotics of correlations in the Ising model: a brief survey. In: Panoramas et synthèses - Société mathématique de France, 2023, vol. 59, p. 157–184.

Article (Accepted version)

Identifiers

PID : unige:117750
arXiv : 1905.06207

Journal ISSN1272-3835

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358downloads

Creation16/05/2019 08:49:00

First validation16/05/2019 08:49:00

Update04/04/2025 12:57:58

Status update28/08/2023 12:12:01

Last indexation04/04/2025 12:58:24

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Asymptotics of correlations in the Ising model: a brief survey

We present a brief survey of rigorous results on the asymptotic behavior of correlations between two local functions as the distance between their support diverges, concentrating on the Ising model on Z^d with finite-range ferromagnetic interactions.

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