On a \(C^ *\)-algebra approach to phase transition in the two-dimensional Ising model. II
type: Item
instance of: scholarly article
title: On a \(C^ *\)-algebra approach to phase transition in the two-dimensional Ising model. II
zbMATH Open document ID: 0608.46041
DOI: 10.1007/BF01221645
author: B. George
published in: Communications in Mathematical Physics
publication date: 1985-01-01T00:00:00Z
review text: We investigate the states \(\phi_{\beta}\) on the \(C^*\)-algebra of Pauli spins on a one-dimensional lattice (infinitely extended in both directions) which give rise to the thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model (with nearest neighbour interaction) at inverse temperature \(\beta\). We show that if \(\beta_ c\) is the known inverse critical temperature, then there exists a family \(\{\nu_{\beta}:\beta \neq \beta_ c\}\) of automorhisms of the Pauli algebra such that \[ \phi_{\beta}=\phi_ 0\circ \nu_{\beta}\;if\;0\leq \beta <\beta_ c\quad and\quad =\phi_{\infty}\circ \nu_{\beta}\;if\;\beta >\beta_ c. \] [For part I see \textit{H. Araki} and the first named author, ibid. 91, 489-503 (1983; Zbl 0535.46046).]
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 46N99
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 3983888
zbMATH Keywords: C\({}^ *\)-algebra of Pauli spins on a one-dimensional lattice
zbMATH Keywords: thermodynamic limit of the Gibbs ensemble in the two-dimensional Ising model
zbMATH Keywords: Pauli algebra
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01221645
OpenAlex ID: W4252877045
description: scientific article; zbMATH DE number 3983888