Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States
A class of general spin $frac{1}{2}$ lattice models on hyper-cubic lattice $Z^d$, whose Hamiltonians are sums of two functions depending on the Pauli matrices $S^1$, $S^2$ and $S^3$, respectively, are found, which have Gibbsian eigen (ground) states and two order parameters for two spin components $...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2006-01-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Online Access: | http://www.emis.de/journals/SIGMA/2006/Paper011/ |
| _version_ | 1819099235568582656 |
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| author | Wolodymyr Skrypnik |
| author_facet | Wolodymyr Skrypnik |
| author_sort | Wolodymyr Skrypnik |
| collection | DOAJ |
| description | A class of general spin $frac{1}{2}$ lattice models on hyper-cubic lattice $Z^d$, whose Hamiltonians are sums of two functions depending on the Pauli matrices $S^1$, $S^2$ and $S^3$, 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 $alpha$ playing the role of the inverse temperature. It is shown that the ferromagnetic order in $x$ direction exists for all dimensions $dgeq 1$ for a wide class of considered models (a proof is remarkably simple). |
| first_indexed | 2024-12-22T00:43:39Z |
| format | Article |
| id | doaj.art-4932a8f5d3d644ef9899b54889a966da |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-22T00:43:39Z |
| publishDate | 2006-01-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-4932a8f5d3d644ef9899b54889a966da2022-12-21T18:44:36ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592006-01-012011Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground StatesWolodymyr SkrypnikA class of general spin $frac{1}{2}$ lattice models on hyper-cubic lattice $Z^d$, whose Hamiltonians are sums of two functions depending on the Pauli matrices $S^1$, $S^2$ and $S^3$, 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 $alpha$ playing the role of the inverse temperature. It is shown that the ferromagnetic order in $x$ direction exists for all dimensions $dgeq 1$ for a wide class of considered models (a proof is remarkably simple).http://www.emis.de/journals/SIGMA/2006/Paper011/Gibbsian eigen (ground) statesquantum spin models |
| spellingShingle | Wolodymyr Skrypnik Order Parameters in XXZ-Type Spin 1/2 Quantum Models with Gibbsian Ground States Symmetry, Integrability and Geometry: Methods and Applications Gibbsian eigen (ground) states quantum spin models |
| 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 |
| topic | Gibbsian eigen (ground) states quantum spin models |
| url | http://www.emis.de/journals/SIGMA/2006/Paper011/ |
| work_keys_str_mv | AT wolodymyrskrypnik orderparametersinxxztypespin12quantummodelswithgibbsiangroundstates |