Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model
The inhomogeneous six-vertex model is a 2 multiparametric integrable statistical system. In the scaling limit, it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions, the...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211163 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model. Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval and Sergei L. Lukyanov. SIGMA 17 (2021), 025, 29 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862589800271314944 |
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| author | Bazhanov, Vladimir V. Kotousov, Gleb A. Koval, Sergii M. Lukyanov, Sergei L. |
| author_facet | Bazhanov, Vladimir V. Kotousov, Gleb A. Koval, Sergii M. Lukyanov, Sergei L. |
| citation_txt | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model. Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval and Sergei L. Lukyanov. SIGMA 17 (2021), 025, 29 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The inhomogeneous six-vertex model is a 2 multiparametric integrable statistical system. In the scaling limit, it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions, the model possesses U(1) invariance. In this paper, we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of , , and as well as translational invariance. The special properties of the lattice system that possesses an additional ᵣ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model.
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| first_indexed | 2026-03-13T19:51:27Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211163 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-13T19:51:27Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
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| spelling | Bazhanov, Vladimir V. Kotousov, Gleb A. Koval, Sergii M. Lukyanov, Sergei L. 2025-12-25T13:18:45Z 2021 Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model. Vladimir V. Bazhanov, Gleb A. Kotousov, Sergii M. Koval and Sergei L. Lukyanov. SIGMA 17 (2021), 025, 29 pages 1815-0659 2020 Mathematics Subject Classification: 16T25; 52C26; 81T40; 82B20; 82B23 arXiv:2010.10615 https://nasplib.isofts.kiev.ua/handle/123456789/211163 https://doi.org/10.3842/SIGMA.2021.025 The inhomogeneous six-vertex model is a 2 multiparametric integrable statistical system. In the scaling limit, it is expected to cover different classes of critical behaviour which, for the most part, have remained unexplored. For general values of the parameters and twisted boundary conditions, the model possesses U(1) invariance. In this paper, we discuss the restrictions imposed on the parameters for which additional global symmetries arise that are consistent with the integrable structure. These include the lattice counterparts of , , and as well as translational invariance. The special properties of the lattice system that possesses an additional ᵣ invariance are considered. We also describe the Hermitian structures, which are consistent with the integrable one. The analysis lays the groundwork for studying the scaling limit of the inhomogeneous six-vertex model. The authors thank R.J. Baxter for providing details of the Bethe ansatz for the six-vertex model on the 45-rotated square lattice [2] and N.Yu. Reshetikhin for important comments. VB acknowledges the support of the Australian Research Council grant DP180101040. The research of GK is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germanys Excellence Strategy EXC 2121 Quantum Universe 390833306. The research of SL is supported by the Rutgers New High Energy Theory Center. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model Article published earlier |
| spellingShingle | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model Bazhanov, Vladimir V. Kotousov, Gleb A. Koval, Sergii M. Lukyanov, Sergei L. |
| title | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model |
| title_full | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model |
| title_fullStr | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model |
| title_full_unstemmed | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model |
| title_short | Some Algebraic Aspects of the Inhomogeneous Six-Vertex Model |
| title_sort | some algebraic aspects of the inhomogeneous six-vertex model |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211163 |
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