Attractiveness of interactions for binary lattice systems and the global Markov property
type: Item
instance of: scholarly article
title: Attractiveness of interactions for binary lattice systems and the global Markov property
zbMATH Open document ID: 0636.60107
DOI: 10.1016/0304-4149(87)90021-4
published in: Stochastic Processes and their Applications
publication date: 1987-01-01T00:00:00Z
review text: The author gives a necessary and sufficient condition for the nearest neighbor pair interaction to be attractive with respect to some order on the states of binary lattice systems. In virtue of \textit{H. Fölmer}'s recent result on attractive interactions [Quantum fields-algebras, processes, Proc. Symp., Bielefeld 1978, 293-302 (1980; Zbl 0457.60077)], this implies that if a nearest neighbor translation invariant interaction on a square lattice generates a unique Gibbs state, the latter possesses the global Markov property.
Mathematics Subject Classification ID: 60K35
zbMATH DE Number: 4036889
zbMATH Keywords: nearest neighbor pair interaction
zbMATH Keywords: Gibbs state
zbMATH Keywords: global Markov property
author: Christoph W. Keßler
MaRDI profile type: Publication
full work available at URL: 0304-4149(87)90021-4
OpenAlex ID: W2054792582
cites work: The global Markov property for lattice systems
cites work: The problem of uniqueness of a Gibbsian random field and the problem of phase transitions
cites work: Q3782526
cites work: Some examples concerning the global Markov property
cites work: Q4130180
description: scientific article; zbMATH DE number 4036889