Non-Gibbsianness of the reduced SOS-measure
type: Item
instance of: scholarly article
title: Non-Gibbsianness of the reduced SOS-measure
zbMATH Open document ID: 0927.60079
DOI: 10.1016/S0304-4149(97)00107-5
published in: Stochastic Processes and their Applications
publication date: 1999-11-18T00:00:00Z
review text: Let \(\rho \) be a Gibbs probability measure on the configuration space \(\Omega ={\mathbb Z}^{{\mathbb Z}^d}\) which corresponds to the pair potential (\(\omega \in \Omega \), \(i,j\in {\mathbb Z}^d\)) \[ \psi_{i,j}(\omega)=J | \omega_i-\omega_j| \;\text{ if }| i-j| =1 \] (and 0 otherwise) with constant \(J>0\). The author shows that the image of \(\rho \) under the mapping \(F:\Omega \to \{-1,1\}^{{\mathbb Z}^d}\), \(F(\omega_i)=1\) if \(\omega_i\geq 0\) and \(F(\omega_i)=-1\) otherwise, is not a Gibbs measure with respect to any translation invariant interaction model on \(\{-1,1\}^{{\mathbb Z}^d}\). The proof uses the concept of relative entropy densities.
reviewed by: Jan Rataj
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 60G60
zbMATH DE Number: 1364458
zbMATH Keywords: Gibbs probability measure
zbMATH Keywords: pair interaction model
zbMATH Keywords: relative entropy density
author: József Lorinczi
MaRDI profile type: Publication
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full work available at URL: s0304-4149(97)00107-5
OpenAlex ID: W2127118625
description: scientific article; zbMATH DE number 1364458