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Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States

Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States

Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magneti...

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Main Authors: Dorlas, T.C., Skrypnik, W.I.
Format: Article
Language:English
Published: Інститут математики НАН України 2008
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/149000
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spelling irk-123456789-1490002019-02-20T01:25:16Z Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States Dorlas, T.C. Skrypnik, W.I. Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state. 2008 Article Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 82B10; 82B20; 82B26 http://dspace.nbuv.gov.ua/handle/123456789/149000 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description Quantum models on the hyper-cubic d-dimensional lattice of spin-1/2 particles interacting with linear oscillators are shown to have three ferromagnetic ground state order parameters. Two order parameters coincide with the magnetization in the first and third directions and the third one is a magnetization in a continuous oscillator variable. The proofs use a generalized Peierls argument and two Griffiths inequalities. The class of spin-oscillator Hamiltonians considered manifest maximal ordering in their ground states. The models have relevance for hydrogen-bond ferroelectrics. The simplest of these is proven to have a unique Gibbsian ground state.
format Article
author Dorlas, T.C.
Skrypnik, W.I.
spellingShingle Dorlas, T.C.
Skrypnik, W.I.
Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Dorlas, T.C.
Skrypnik, W.I.
author_sort Dorlas, T.C.
title Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_short Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_full Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_fullStr Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_full_unstemmed Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States
title_sort three order parameters in quantum xz spin-oscillator models with gibbsian ground states
publisher Інститут математики НАН України
publishDate 2008
url http://dspace.nbuv.gov.ua/handle/123456789/149000
citation_txt Three Order Parameters in Quantum XZ Spin-Oscillator Models with Gibbsian Ground States / T.C. Dorlas, W.I. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 29 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT dorlastc threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates
AT skrypnikwi threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates
first_indexed 2023-05-20T17:31:59Z
last_indexed 2023-05-20T17:31:59Z
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