Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States
A class of general spin 1/2 lattice models on hyper-cubic lattice Zd, whose Hamiltonians are sums of two functions depending on the Pauli matrices S¹, S² and S³, respectively, are found, which have Gibbsian eigen (ground) states and two order parameters for two spin components x, z simultaneously fo...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2006 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146442 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States / W. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862726244509941760 |
|---|---|
| author | Skrypnik, W. |
| author_facet | Skrypnik, W. |
| citation_txt | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States / W. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | A class of general spin 1/2 lattice models on hyper-cubic lattice Zd, whose Hamiltonians are sums of two functions depending on the Pauli matrices S¹, S² and S³, respectively, are found, which have Gibbsian eigen (ground) states and two order parameters for two spin components x, z simultaneously for large values of the parameter α playing the role of the inverse temperature. It is shown that the ferromagnetic order in x direction exists for all dimensions d ≥ 1 for a wide class of considered models (a proof is remarkably simple).
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| first_indexed | 2025-12-07T18:57:15Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146442 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T18:57:15Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Skrypnik, W. 2019-02-09T17:13:09Z 2019-02-09T17:13:09Z 2006 Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States / W. Skrypnik // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 8 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 82B10; 82B20; 82B26 https://nasplib.isofts.kiev.ua/handle/123456789/146442 A class of general spin 1/2 lattice models on hyper-cubic lattice Zd, whose Hamiltonians are sums of two functions depending on the Pauli matrices S¹, S² and S³, respectively, are found, which have Gibbsian eigen (ground) states and two order parameters for two spin components x, z simultaneously for large values of the parameter α playing the role of the inverse temperature. It is shown that the ferromagnetic order in x direction exists for all dimensions d ≥ 1 for a wide class of considered models (a proof is remarkably simple). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States Article published earlier |
| spellingShingle | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States Skrypnik, W. |
| title | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States |
| title_full | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States |
| title_fullStr | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States |
| title_full_unstemmed | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States |
| title_short | Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States |
| title_sort | order parameters in xxz-type spin 1/2 quantum models with gibbsian ground states |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146442 |
| work_keys_str_mv | AT skrypnikw orderparametersinxxztypespin12quantummodelswithgibbsiangroundstates |