Examples of extremal lattice fields without the global Markov property
type: Item
instance of: scholarly article
title: Examples of extremal lattice fields without the global Markov property
zbMATH Open document ID: 0592.60091
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1985-01-01T00:00:00Z
review text: We give two examples that disprove the conjecture [\textit{S. Goldstein}, Commun. Math. Phys. 74, 223-234 (1980; Zbl 0429.60097)] that every extremal Gibbs state on a lattice system has the global Markov property. Both examples live on a two dimensional lattice, and the Gibbs state is not unique. In the first example, the interaction is extended real valued; in the second one it is real valued but unbounded and not translation invariant. For an example with a translation invariant and bounded interaction, on a three dimensional lattice, see \textit{R. B. Israel}, ibid. 105, 669-673 (1986).
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 3951757
zbMATH Keywords: extremal Gibbs state on a lattice system
zbMATH Keywords: global Markov property
zbMATH Keywords: translation invariant
zbMATH Keywords: bounded interaction
author: Christoph W. Keßler
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195178936
OpenAlex ID: W2008796122
cites work: The global Markov property for lattice systems
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cites work: A remark on the global Markov property for the d-dimensional Ising model
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cites work: Random fields
DOI: 10.2977/PRIMS/1195178936
description: scientific article; zbMATH DE number 3951757