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Apparaît dans la collection : ALEA Days 2023 / Journées ALEA 2023

We introduce a family of geometrical lattice models generalising the well-known loop model on the hexagonal lattice. These models have a $U_q(sl_n)$ quantum group symmetry, the loop model being the $n=2$ case. The general models give rise to branching webs and describe, at a special point, the interfaces in $Z_n$ symmetric spin models. We mainly discuss the $n=3$ case of bipartite cubic webs, which is based on the Kuperberg $A_2$ spider. We exhibit a local vertex-model reformulation, analogous to the well-known correspondence between the loop model and the nineteen-vertex model. The local formulation allows us in particular to study the model by means of transfer matrices and conformal field theory. We find that it has a rich phase diagram, including a dense and a dilute phase that generalise those known for the loop model. Based on joint work with Augustin Lafay and Azat Gainutdinov (arXiv:2101.00282 and 2107.10106).

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  • LAFAY, Augustin, GAINUTDINOV, Azat M., et JACOBSEN, Jesper Lykke. Uq (sln) web models and Zn spin interfaces. arXiv preprint arXiv:2101.00282, 2021. - https://doi.org/10.48550/arXiv.2101.00282
  • LAFAY, Augustin, GAINUTDINOV, Azat M., et JACOBSEN, Jesper Lykke. $ U_ {\mathfrak {q}}(\mathfrak {sl} _3) $ web models: Locality, phase diagram and geometrical defects. arXiv preprint arXiv:2107.10106, 2021. - https://doi.org/10.48550/arXiv.2107.10106

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