Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914228954202112 |
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| author | Rigas, Pete |
| author_facet | Rigas, Pete |
| contents | We compute the action-angle coordinates for an Ising type model whose L-operator has been previously studied in the literature by Bazhanov and Sergeev. In comparison to computations with such operators that have been examined previously by the author for the 4-vertex, 6-vertex, and 20-vertex, models, computations for asymptotically approximating a collection of sixteen identities with the Poisson bracket, which together constitute the Poisson structure of the Ising type model, exhibit dependencies upon nearest neighbor interactions. Inspite of the fact that L-operators for the 20-vertex model are defined in terms of combinatorial, and algebraic, constituents unlike such operators for the 6-vertex model which are defined in terms of projectors and Pauli basis elements, L-operators for the Ising-type model can be used for concluding that a model which interpolates between the 6-vertex, and 8-vertex, models is exactly solvable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_01996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models Rigas, Pete Statistical Mechanics Mathematical Physics Probability Exactly Solvable and Integrable Systems 34L25, 60K35 We compute the action-angle coordinates for an Ising type model whose L-operator has been previously studied in the literature by Bazhanov and Sergeev. In comparison to computations with such operators that have been examined previously by the author for the 4-vertex, 6-vertex, and 20-vertex, models, computations for asymptotically approximating a collection of sixteen identities with the Poisson bracket, which together constitute the Poisson structure of the Ising type model, exhibit dependencies upon nearest neighbor interactions. Inspite of the fact that L-operators for the 20-vertex model are defined in terms of combinatorial, and algebraic, constituents unlike such operators for the 6-vertex model which are defined in terms of projectors and Pauli basis elements, L-operators for the Ising-type model can be used for concluding that a model which interpolates between the 6-vertex, and 8-vertex, models is exactly solvable. |
| title | Exact solvability of an Ising-type model, and exact solvability of the 6-vertex, and 8-vertex, models |
| topic | Statistical Mechanics Mathematical Physics Probability Exactly Solvable and Integrable Systems 34L25, 60K35 |
| url | https://arxiv.org/abs/2501.01996 |