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November 2018 Gaussian fluctuations for the classical XY model
Charles M. Newman, Wei Wu
Ann. Inst. H. Poincaré Probab. Statist. 54(4): 1759-1777 (November 2018). DOI: 10.1214/17-AIHP854

Abstract

We study the classical XY model in bounded domains of $\mathbb{Z}^{d}$ with Dirichlet boundary conditions. We prove that when the temperature goes to zero faster than a certain rate as the lattice spacing goes to zero, the fluctuation field converges to a Gaussian white noise. This and related results also apply to a large class of gradient field models.

Nous étudions le modèle XY classique dans un domaine borné de $\mathbb{Z}^{d}$ avec condition de Dirichlet au bord. Nous prouvons que quand la température tend vers 0 suffisamment vite avec le pas du graphe, le champ des fluctuations converge vers le bruit blanc Gaussien. Ce résultat ainsi que les résultats associés s’appliquent aussi à une classe large de modèles de champs gradients.

Citation

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Charles M. Newman. Wei Wu. "Gaussian fluctuations for the classical XY model." Ann. Inst. H. Poincaré Probab. Statist. 54 (4) 1759 - 1777, November 2018. https://doi.org/10.1214/17-AIHP854

Information

Received: 29 December 2016; Accepted: 13 July 2017; Published: November 2018
First available in Project Euclid: 18 October 2018

zbMATH: 06996548
MathSciNet: MR3865656
Digital Object Identifier: 10.1214/17-AIHP854

Subjects:
Primary: 60K35, 82B20
Secondary: 60F17, 60G60

Rights: Copyright © 2018 Institut Henri Poincaré

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Vol.54 • No. 4 • November 2018
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