Continuous and Discrete (Classical) Heisenberg Spin Chain Revised
Most of the work done in the past on the integrability structure of the Classical Heisenberg Spin Chain (CHSC) has been devoted to studying the su(2) case, both at the continuous and at the discrete level. In this paper we address the problem of constructing integrable generalized ''Spin C...
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| Дата: | 2007 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2007
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147831 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Continuous and Discrete (Classical) Heisenberg Spin Chain Revised / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 18 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1478312019-02-17T01:24:47Z Continuous and Discrete (Classical) Heisenberg Spin Chain Revised Ragnisco, O. Zullo, F. Most of the work done in the past on the integrability structure of the Classical Heisenberg Spin Chain (CHSC) has been devoted to studying the su(2) case, both at the continuous and at the discrete level. In this paper we address the problem of constructing integrable generalized ''Spin Chains'' models, where the relevant field variable is represented by a N × N matrix whose eigenvalues are the Nth roots of unity. To the best of our knowledge, such an extension has never been systematically pursued. In this paper, at first we obtain the continuous N × N generalization of the CHSC through the reduction technique for Poisson-Nijenhuis manifolds, and exhibit some explicit, and hopefully interesting, examples for 3 × 3 and 4 × 4 matrices; then, we discuss the much more difficult discrete case, where a few partial new results are derived and a conjecture is made for the general case. 2007 Article Continuous and Discrete (Classical) Heisenberg Spin Chain Revised / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 18 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 37K05; 37K10 http://dspace.nbuv.gov.ua/handle/123456789/147831 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 |
Most of the work done in the past on the integrability structure of the Classical Heisenberg Spin Chain (CHSC) has been devoted to studying the su(2) case, both at the continuous and at the discrete level. In this paper we address the problem of constructing integrable generalized ''Spin Chains'' models, where the relevant field variable is represented by a N × N matrix whose eigenvalues are the Nth roots of unity. To the best of our knowledge, such an extension has never been systematically pursued. In this paper, at first we obtain the continuous N × N generalization of the CHSC through the reduction technique for Poisson-Nijenhuis manifolds, and exhibit some explicit, and hopefully interesting, examples for 3 × 3 and 4 × 4 matrices; then, we discuss the much more difficult discrete case, where a few partial new results are derived and a conjecture is made for the general case. |
| format |
Article |
| author |
Ragnisco, O. Zullo, F. |
| spellingShingle |
Ragnisco, O. Zullo, F. Continuous and Discrete (Classical) Heisenberg Spin Chain Revised Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Ragnisco, O. Zullo, F. |
| author_sort |
Ragnisco, O. |
| title |
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised |
| title_short |
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised |
| title_full |
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised |
| title_fullStr |
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised |
| title_full_unstemmed |
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised |
| title_sort |
continuous and discrete (classical) heisenberg spin chain revised |
| publisher |
Інститут математики НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147831 |
| citation_txt |
Continuous and Discrete (Classical) Heisenberg Spin Chain Revised / O. Ragnisco, F. Zullo // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 18 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT ragniscoo continuousanddiscreteclassicalheisenbergspinchainrevised AT zullof continuousanddiscreteclassicalheisenbergspinchainrevised |
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2025-07-11T02:55:33Z |
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2025-07-11T02:55:33Z |
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1837317524225523712 |