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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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2008 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2008
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149000 |
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| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149000 |
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dspace |
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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 |
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AT dorlastc threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates AT skrypnikwi threeorderparametersinquantumxzspinoscillatormodelswithgibbsiangroundstates |
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2023-05-20T17:31:59Z |
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2023-05-20T17:31:59Z |
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1796153517246775296 |