The global Markov property for equilibrium states which are determined by correlations in a strip
type: Item
instance of: scholarly article
title: The global Markov property for equilibrium states which are determined by correlations in a strip
zbMATH Open document ID: 0639.60107
DOI: 10.1007/BF01466768
published in: Communications in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: Consider an interaction-round-face potential on the lattice \({\mathbb{Z}}^ d\), which may include nearest-neighbor and next-nearest-neighbor pair interactions, as well as more general plaquette terms. Assuming some periodicity of the potential it is shown that, under the condition that equilibrium states can be distinguished by expectation values of sufficiently local observables, equilibrium states possess a global Markov property. The condition under which this Markov property is shown to hold is met in particular in case the equilibrium state is unique or determined by the magnetization. The proof is based on an application of the variational principle to states which are constructed like Markov chains.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B05
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4043021
zbMATH Keywords: nearest-neighbor and next-nearest-neighbor pair interactions
zbMATH Keywords: global Markov property
zbMATH Keywords: variational principle
author: Roelof Kuik
MaRDI profile type: Publication
cites work: Remarks on the global Markov property
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cites work: Q4185090
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description: scientific article; zbMATH DE number 4043021