Solving the n-color ice model
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arXiv
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| Main Authors: | , , , , , , , , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
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| _version_ | 1866915417854836736 |
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| author | Addona, Patrick Bockenhauer, Ethan Brubaker, Ben Cauthorn, Michael Conefrey-Shinozaki, Cianan Donze, David Dudarov, William Dukes, Jessamyn Hardt, Andrew Li, Cindy Li, Jigang Liu, Yanli Puthanveetil, Neelima Qudsi, Zain Simons, Jordan Sullivan, Joseph Young, Autumn |
| author_facet | Addona, Patrick Bockenhauer, Ethan Brubaker, Ben Cauthorn, Michael Conefrey-Shinozaki, Cianan Donze, David Dudarov, William Dukes, Jessamyn Hardt, Andrew Li, Cindy Li, Jigang Liu, Yanli Puthanveetil, Neelima Qudsi, Zain Simons, Jordan Sullivan, Joseph Young, Autumn |
| contents | Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the Yang-Baxter equation. Furthermore we provide an explicit one-dimensional parametrization of all solutions in this case. These $n$-color lattice models are so named because their admissible vertices have adjacent edges labeled by one of $n$ colors with additional restrictions. The two-colored case specializes to the six-vertex model, in which case our results recover the familiar quadric condition of Baxter for solvability. The general $n$-color case includes important solutions to the Yang-Baxter equation like the evaluation modules for the quantum affine Lie algebra $U_q(\hat{\mathfrak{sl}}_n)$. Finally, we demonstrate the invariance of this class of solutions under natural transformations, including those associated with Drinfeld twisting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_06404 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Solving the n-color ice model Addona, Patrick Bockenhauer, Ethan Brubaker, Ben Cauthorn, Michael Conefrey-Shinozaki, Cianan Donze, David Dudarov, William Dukes, Jessamyn Hardt, Andrew Li, Cindy Li, Jigang Liu, Yanli Puthanveetil, Neelima Qudsi, Zain Simons, Jordan Sullivan, Joseph Young, Autumn Mathematical Physics Combinatorics Representation Theory 16T25 (Primary), 82B23, 20G42, 05E10 (secondary) Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the Yang-Baxter equation. Furthermore we provide an explicit one-dimensional parametrization of all solutions in this case. These $n$-color lattice models are so named because their admissible vertices have adjacent edges labeled by one of $n$ colors with additional restrictions. The two-colored case specializes to the six-vertex model, in which case our results recover the familiar quadric condition of Baxter for solvability. The general $n$-color case includes important solutions to the Yang-Baxter equation like the evaluation modules for the quantum affine Lie algebra $U_q(\hat{\mathfrak{sl}}_n)$. Finally, we demonstrate the invariance of this class of solutions under natural transformations, including those associated with Drinfeld twisting. |
| title | Solving the n-color ice model |
| topic | Mathematical Physics Combinatorics Representation Theory 16T25 (Primary), 82B23, 20G42, 05E10 (secondary) |
| url | https://arxiv.org/abs/2212.06404 |