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

Abstract

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 N4 dimensional space VN⊗VN⊗VN⊗VN, appropriate for consideration by means of the cube-equations 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.