Explicit R-matrices for inhomogeneous 3D chiral Potts models: Integrability and the action formulation for IM

We construct the exact spectral parameter dependent vertex R-matrix for the classical 3D N-state chiral Potts models, convenient for considering the model in context of the Bethe ansatz. The R-matrix is defined on the N-4 dimensional space V-N circle times V-N circle times V-N circle times V-N, appropriate for consideration by means of the cubeequations defined in Khachatryan et al. (2015). We present the 2D quantum spin Hamiltonians for general case and, at N = 2, a fermionic lattice action representation corresponding to 3D Ising's statistical model. (C) 2021 Elsevier Inc. All rights reserved.

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We construct the exact spectral parameter dependent vertex R-matrix for the classical 3D N-state chiral Potts models, convenient for considering the model in the context of the Bethe ansatz. The R-matrix is defined on the N-4 dimensional space V-N circle times V-N circle times V-N circle times V-N, appropriate for consideration by means of the cubeequations defined in Khachatryan et al. (2015). We present the 2D quantum spin Hamiltonians for the general case and, at N = 2, a fermionic lattice action representation corresponding to 3D Ising's statistical model.