On the absence of phase transition in continuous one-dimensional Gibbs systems with no hard core
type: Item
instance of: scholarly article
title: On the absence of phase transition in continuous one-dimensional Gibbs systems with no hard core
zbMATH Open document ID: 0591.60097
DOI: 10.1007/BF00363511
publication date: 1987-01-01T00:00:00Z
review text: It has been known for some time that one-dimensional continuous Gibbs systems specified by long range hard core pair potentials exhibit no phase transition, i.e. are uniquely determined by the potential, provided the tail of the potential has a finite first moment. The present paper deals with long range potentials which have no hard core but diverge appropriately at zero, and proves that they admit unique ''regular'' Gibbs systems at arbitrary temperature and activity level. Regularity here means that the expected numbers of particles in intervals of equal length are uniformly bounded.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
zbMATH DE Number: 3949462
zbMATH Keywords: Gibbs systems
zbMATH Keywords: pair potentials
zbMATH Keywords: long range potentials
author: F. Papangelou
MaRDI profile type: Publication
cites work: One-dimensional DLR invariant measures are regular
cites work: CONDITIONS FOR THE ABSENCE OF PHASE TRANSITIONS IN ONE-DIMENSIONAL CLASSICAL SYSTEMS
cites work: On the absence of phase transition in one-dimensional random fields
cites work: Random fields
cites work: Superstable interactions in classical statistical mechanics
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 3949462