On different approaches to integrable lattice models II

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 Inter...

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Bibliographic Details
Main Authors Belavin, Vladimir, Gepner, Doron, Cabezas, Juan Ramos, Runov, Boris
Format Journal Article
LanguageEnglish
Published 09.09.2024
Subjects
Physics - High Energy Physics - Theory
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Summary: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.
DOI:10.48550/arxiv.2409.05637