Ergodicity of the hard-core model on \(\mathbb{Z}^ 2\) with parity-dependent activities
type: Item
instance of: scholarly article
title: Ergodicity of the hard-core model on \(\mathbb{Z}^ 2\) with parity-dependent activities
zbMATH Open document ID: 0874.60097
DOI: 10.1007/BF02559597
author: Olle Häggström
published in: Arkiv för Matematik
publication date: 1997-11-02T00:00:00Z
review text: Consider the hard-core model on \(\mathbb{Z}^2\) with activities \(a_e\) on the even lattice and \(a_o\) on the odd lattice. It is an old result due to Dobrushin that in the symmetric case \(a_e=a_o=a\) with \(a\) sufficiently large, the system exhibits a phase transition. We show that this does not happen when \(a_e\neq a_o\), thereby confirming the two-dimensional case of a conjecture by van den Berg and Steif.
Mathematics Subject Classification ID: 60K40
Mathematics Subject Classification ID: 82D05
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 60K30
zbMATH DE Number: 1031492
zbMATH Keywords: hard-core model
zbMATH Keywords: phase transition
zbMATH Keywords: ergodicity
zbMATH Keywords: percolation
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02559597
OpenAlex ID: W2072678675
description: scientific article; zbMATH DE number 1031492