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 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.