Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions
type: Item
instance of: scholarly article
title: Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions
zbMATH Open document ID: 0668.60093
DOI: 10.1007/BF01238808
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: We give a general method for proving uniqueness and global Markov property for Euclidean quantum fields. The method is based on uniform continuity of local specifications (proved by usig potential theoretical tools) and exploitation of a suitable FKG-order structure. We apply this method to give a proof of uniqueness and global Markov property for the Gibbs states and to study extremality of Gibbs states also in the case of non-uniqueness. In particular we prove extremality for \(\phi^ 4_ 2\) (also in the case of non-uniqueness), and global Markov property for weak coupling \(\phi^ 4_ 2\) (which solves a long- standing problem). Uniqueness and extremality holds also at any point of differentiability of the pressure with respect to the external magnetic field.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 81P20
Mathematics Subject Classification ID: 60J99
zbMATH DE Number: 4094556
zbMATH Keywords: global Markov property for Euclidean quantum fields
zbMATH Keywords: extremality of Gibbs states
author: S. Albeverio
author: Raphael Høegh-Krohn
author: Boguslaw Zegarliński
MaRDI profile type: Publication
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Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions (full work available at URL)
full work available at URL: https://doi.org/10.1007/bf01238808

Uniqueness and global Markov property for Euclidean fields: The case of general polynomial interactions (OpenAlex ID)
OpenAlex ID: W2028693397