Large-deviation principle for one-dimensional vector spin models with Kac potentials
type: Item
instance of: scholarly article
title: Large-deviation principle for one-dimensional vector spin models with Kac potentials
zbMATH Open document ID: 0942.60098
DOI: 10.1023/A:1023095619236
author: Paolo Buttà
author: Pierre Picco
published in: Journal of Statistical Physics
publication date: 2000-08-16T00:00:00Z
review text: This paper studies planar rotor and classical Heisenberg models with Kac interactions in one dimension. The results concern first the classical Lebowitz-Penrose theorem, that states that the free energy as a function of the total magnetization vector converges to the convex hull of the corresponding function of the related mean field model. The second, and more difficult result of the paper is an upper estimate on the scale over which the ``mesoscopic magnetization profiles'' are Gibbs-typically constant. If \(\gamma^{-1}\) is the range of the interaction, it is found that this scale is larger than \(\gamma^{-1-\lambda}\) with some positive \(\lambda\). (Note that it is expected that such a result should be true with \(\lambda=1\).) Results of this type have first been obtained in the Kac-Ising model by \textit{M. Cassandro, E. Orlandi} and \textit{E. Presutti} [Probab. Theory Relat. Fields 96, No. 1, 57-96 (1993; Zbl 0791.60096)].
reviewed by: Anton Bovier
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 82B20
zbMATH DE Number: 1357842
zbMATH Keywords: Kac potentials
zbMATH Keywords: spin vector models
MaRDI profile type: Publication
full work available at URL: a:1023095619236
OpenAlex ID: W1589862320
description: scientific article; zbMATH DE number 1357842