On the XY-model on two-sided infinite chain
type: Item
instance of: scholarly article
title: On the XY-model on two-sided infinite chain
zbMATH Open document ID: 0544.46040
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1984-01-01T00:00:00Z
review text: The XY-model on the one-dimensional lattice, infinitely extended to both directions, is studied by a method of \(C^*\)-algebra. The following three features are found different from the same model on one-sided infinite chain studied by \textit{H. Araki} and \textit{E. Barouch} [J. Stat. Phys. 31, 327-345 (1983)]: (1) There are no non-trivial constant observables. (2) The (twisted) asymptotic abelian property holds only partially and not for general observable operators. (3) Return to equilibrium occurs for all values of the parameter \(\gamma\) and is proved by a method different from the case of one-sided chain.
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 82B10
zbMATH DE Number: 3865988
zbMATH Keywords: spin lattice systems
zbMATH Keywords: asymptotic abelian
zbMATH Keywords: canonical anticommutation relations
zbMATH Keywords: XY-model
zbMATH Keywords: Return to equilibrium
author: Huzihiro Araki
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195181608
OpenAlex ID: W2073911581
cites work: Q3913911
cites work: Relaxation of Local Thermal Deviations from Equilibrium
cites work: Return to equilibrium
cites work: On the dynamics and ergodic properties of the XY model
cites work: Two soluble models of an antiferromagnetic chain
cites work: Dissipations and derivations
cites work: On uniqueness of KmMS states of one-dimensional quantum lattice systems
cites work: On uniqueness of KMS states of one-dimensional quantum lattice systems
cites work: Q5526485
cites work: On quasifree states of CAR and Bogoliubov automorphisms
DOI: 10.2977/PRIMS/1195181608
description: scientific article; zbMATH DE number 3865988