Embedding integrable spin models in solvable vertex models on the square lattice
Exploring a mapping among n-state spin and vertex models on the square lattice, we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be formulated in the framework of an equivalent solvable vertex model. The Lax operator and the R-matrix assoc...
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Elsevier
2025-04-01
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| Series: | Nuclear Physics B |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325000586 |
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| author | M.J. Martins |
| author_facet | M.J. Martins |
| author_sort | M.J. Martins |
| collection | DOAJ |
| description | Exploring a mapping among n-state spin and vertex models on the square lattice, we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be formulated in the framework of an equivalent solvable vertex model. The Lax operator and the R-matrix associated to the vertex model are built in terms of the edge weights of the spin model and these operators are shown to satisfy the Yang-Baxter algebra. The unitarity of the R-matrix follows from an assumption that the vertical edge weights of the spin model satisfy certain local identities known as inversion relation. We apply this embedding to the scalar n-state Potts model and we argue that the corresponding R-matrix can be written in terms of the underlying Temperley-Lieb operators. We also consider our construction for the integrable Ashkin-Teller model and the respective R-matrix is expressed in terms of sixteen distinct weights parametrized by theta functions. We comment on the possible extension of our results to spin models whose edge weights are not expressible in terms of the difference of spectral parameters. |
| format | Article |
| id | doaj-art-c1c08ea46431496680b1467bc0c51136 |
| institution | DOAJ |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-c1c08ea46431496680b1467bc0c511362025-08-20T02:48:03ZengElsevierNuclear Physics B0550-32132025-04-01101311684910.1016/j.nuclphysb.2025.116849Embedding integrable spin models in solvable vertex models on the square latticeM.J. Martins0Universidade Federal de São Carlos, Departamento de Física, C.P. 676, 13565-905, São Carlos (SP), BrazilExploring a mapping among n-state spin and vertex models on the square lattice, we argue that a given integrable spin model with edge weights satisfying the rapidity difference property can be formulated in the framework of an equivalent solvable vertex model. The Lax operator and the R-matrix associated to the vertex model are built in terms of the edge weights of the spin model and these operators are shown to satisfy the Yang-Baxter algebra. The unitarity of the R-matrix follows from an assumption that the vertical edge weights of the spin model satisfy certain local identities known as inversion relation. We apply this embedding to the scalar n-state Potts model and we argue that the corresponding R-matrix can be written in terms of the underlying Temperley-Lieb operators. We also consider our construction for the integrable Ashkin-Teller model and the respective R-matrix is expressed in terms of sixteen distinct weights parametrized by theta functions. We comment on the possible extension of our results to spin models whose edge weights are not expressible in terms of the difference of spectral parameters.http://www.sciencedirect.com/science/article/pii/S0550321325000586Spin and vertex modelsIntegrabilityYang-Baxter equation |
| spellingShingle | M.J. Martins Embedding integrable spin models in solvable vertex models on the square lattice Nuclear Physics B Spin and vertex models Integrability Yang-Baxter equation |
| title | Embedding integrable spin models in solvable vertex models on the square lattice |
| title_full | Embedding integrable spin models in solvable vertex models on the square lattice |
| title_fullStr | Embedding integrable spin models in solvable vertex models on the square lattice |
| title_full_unstemmed | Embedding integrable spin models in solvable vertex models on the square lattice |
| title_short | Embedding integrable spin models in solvable vertex models on the square lattice |
| title_sort | embedding integrable spin models in solvable vertex models on the square lattice |
| topic | Spin and vertex models Integrability Yang-Baxter equation |
| url | http://www.sciencedirect.com/science/article/pii/S0550321325000586 |
| work_keys_str_mv | AT mjmartins embeddingintegrablespinmodelsinsolvablevertexmodelsonthesquarelattice |