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arXiv · 2409.05637

On different approaches to integrable lattice models II

Vladimir Belavin·Doron Gepner·Juan Ramos Cabezas·Boris Runov
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Abstract

This paper represents a continuation of our previous work, where the Bolzmann weights (BWs) for several Interaction-Round-the Face (IRF) lattice models were computed using their relation to rational conformal field theories. Here, we focus on deriving solutions for the Boltzmann weights of the Interaction-Round the Face lattice model, specifically the unrestricted face model, based on the $\mathfrak{su}(3)_k$ affine Lie algebra. The admissibility conditions are defined by the adjoint representation. We find the BWs by determining the quantum $R$ matrix of the $U_q(\mathfrak{sl} (3))$ quantum algebra in the adjoint representation and then applying the so-called Vertex-IRF correspondence. The Vertex-IRF correspondence defines the BWs of IRF models in terms of $R$ matrix elements.

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Vladimir Belavin, Doron Gepner, Juan Ramos Cabezas, Boris Runov. 2024-09-09. On different approaches to integrable lattice models II. https://arxiv.org/abs/2409.05637

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