Intertwining vectors, and Boltzmann weight matrices, of a Solid-on-Solid model from the 20-vertex model
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| Format: | Preprint |
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2024
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| _version_ | 1866908422091309056 |
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| author | Rigas, Pete |
| author_facet | Rigas, Pete |
| contents | We initiate a new study on the correspondence between the 20-vertex model and a SOS (Solid-on-Solid) model. In comparison to two previous works of the author in 2024 which characterized properties of the transfer, and quantum monodromy, matrices of the 20-vertex model from the perspective of the quantum inverse scattering method, in addition to the structure of nonlocal correlations, the forthcoming approach is an adaptation of a study on the rational 7-vertex model. For the rational 7-vertex model, Antoenneko and Valinevich demonstrated that the intertwining vectors can be used to transform the R-matrix of a vertex model into the Boltzman weight matrix of an SOS model. To further develop perspectives on classes of higher dimensional SOS models, by leveraging previous computations with L-operators due to the author, and by also manipulating q-exponentials, and other related factors from a factorization of the universal R-matrix due to Boos et al, analogs of intertwining vectors for the 20- vertex model can be obtained. In comparison to the system of equations that have been obtained for the rational 7-vertex model, the system that one obtains for the 20-vertex model consists of 9 equations for each entry of the R-matrix. Furthermore, from the fact that the 20-vertex model contains more possible configurations in the sample space than the rational 7-vertex model does, the Boltzman weight matrix of the corresponding SOS model asymptotically depends upon several contributions, a few of which include tensor products of basis elements, and spectral parameters over the triangular lattice. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_04515 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Intertwining vectors, and Boltzmann weight matrices, of a Solid-on-Solid model from the 20-vertex model Rigas, Pete Mathematical Physics Probability 34L25, 60K35 We initiate a new study on the correspondence between the 20-vertex model and a SOS (Solid-on-Solid) model. In comparison to two previous works of the author in 2024 which characterized properties of the transfer, and quantum monodromy, matrices of the 20-vertex model from the perspective of the quantum inverse scattering method, in addition to the structure of nonlocal correlations, the forthcoming approach is an adaptation of a study on the rational 7-vertex model. For the rational 7-vertex model, Antoenneko and Valinevich demonstrated that the intertwining vectors can be used to transform the R-matrix of a vertex model into the Boltzman weight matrix of an SOS model. To further develop perspectives on classes of higher dimensional SOS models, by leveraging previous computations with L-operators due to the author, and by also manipulating q-exponentials, and other related factors from a factorization of the universal R-matrix due to Boos et al, analogs of intertwining vectors for the 20- vertex model can be obtained. In comparison to the system of equations that have been obtained for the rational 7-vertex model, the system that one obtains for the 20-vertex model consists of 9 equations for each entry of the R-matrix. Furthermore, from the fact that the 20-vertex model contains more possible configurations in the sample space than the rational 7-vertex model does, the Boltzman weight matrix of the corresponding SOS model asymptotically depends upon several contributions, a few of which include tensor products of basis elements, and spectral parameters over the triangular lattice. |
| title | Intertwining vectors, and Boltzmann weight matrices, of a Solid-on-Solid model from the 20-vertex model |
| topic | Mathematical Physics Probability 34L25, 60K35 |
| url | https://arxiv.org/abs/2412.04515 |