Year: 2024
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Belavin, Vladimir, Gepner, Doron, Cabezas, Juan Ramos, Runov, Boris
Institutions: Ariel University, Weizmann Institute of Science
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403618664