Convergence of grand canonical Gibbs measures
type: Item
instance of: scholarly article
title: Convergence of grand canonical Gibbs measures
zbMATH Open document ID: 0538.60095
DOI: 10.1007/BF01210724
author: David Klein
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: The paper tries to prove existence of Gibbs states in continuum systems by adding a hard-core N-body potential with fixed radius and then letting N tend to infinity. In the presence of such a hard-core the existence is established, but unfortunately there is an error in the proof ot the crucial approximation lemma 3.1. More precisely, the inequality (3.10) does not hold uniformly in k except in the one-dimensional case. A note of this mistake is given also by the author in the paper ''Uniqueness of one dimensional continuum Gibbs states'', to appear in Commun. Math. Phys. However, since there is no counterexample, it remains open if such an approximation by hard-core potentials is possible or not.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60G60
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3856169
zbMATH Keywords: existence of thermodynamic limit
zbMATH Keywords: existence of Gibbs states
zbMATH Keywords: hard-core potentials
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01210724
OpenAlex ID: W1969901225
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description: scientific article; zbMATH DE number 3856169