Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion
type: Item
instance of: scholarly article
title: Uniqueness of Gibbs states for general \(P(\phi)_ 2\)-weak coupling models by cluster expansion
zbMATH Open document ID: 0698.60093
DOI: 10.1007/BF01218163
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: Quantum fields with weak coupling in two space-time dimensions are considered. The basic theorem of this paper states that for general \(P(\phi)_ 2\)-weak coupling models with sufficiently small coupling constant the set of all ultra regular Gibbs states consists only of one point which is an extremal Gibbs state. In the proof are used the method of cluster expansion in the sense of Glimm, Jaffé and Spencer, as well as the estimates of the solutions of the Dirichlet problem with distributional data and the representation of ultra regular measures in the sense of \textit{J. Fröhlich} and \textit{B. Simon} [see Ann. Math. 105, 493-526 (1977)].
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 4145102
zbMATH Keywords: Quantum fields with weak coupling
zbMATH Keywords: ultra regular Gibbs states
zbMATH Keywords: extremal Gibbs state
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: ultra regular measures
author: S. Albeverio
author: Raphael Høegh-Krohn
author: Boguslaw Zegarliński
reviewed by: S. Poghosyan
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01218163
OpenAlex ID: W1485118991
description: scientific article; zbMATH DE number 4145102