Large deviations in the van der Waals limit
type: Item
instance of: scholarly article
title: Large deviations in the van der Waals limit
zbMATH Open document ID: 0927.60080
DOI: 10.1016/S0304-4149(98)00002-7
author: O. Benois
author: Thierry Bodineau
author: Errico Presutti
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: The main result is a strong large deviation principle for the empirical distribution of Ising spins in the 2-dimensional Ising system with the Kac potential and the scaling parameter \(\gamma \) at temperatures less than the critical one. It is studied in the thermodynamic limit followed by the limit for the scaling parameter \(\gamma >0\) tending to zero. Results of the paper by the authors and \textit{P. Buttà} [Markov Process. Relat. Fields 3, No. 2, 175-198 (1997; Zbl 0910.60014)], where interfaces were studied and a weak form of the large deviation principle was established, are used. The proof of the strong version needs moreover an estimate called ``exponential tightness''. Its proof is based on a reformulation in terms of contours for some auxiliary block-spin model, the study of contours, and some Peierls estimates.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 60F10
zbMATH DE Number: 1364474
zbMATH Keywords: Kac potentials
zbMATH Keywords: large deviations
zbMATH Keywords: interfaces
zbMATH Keywords: surface tension
reviewed by: Petr Holický
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1364474