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

Abstract

We construct the exact spectral parameter dependent vertex R-matrix for the classical 3D $\mathcal{N}$-state chiral Potts models, convenient for considering the model in context of the Bethe ansatz. The R-matrix is defined on the ${\mathcal{N}}^4$ dimensional space $V_{\mathcal{N}}\otimes V_{\mathcal{N}}\otimes V_{\mathcal{N}}\otimes V_{\mathcal{N}}$, appropriate for consideration by means of the cube-equations defined in [14]. We present the 2D quantum spin Hamiltonians for general case and, at $\mathcal{N}=2$, a fermionic lattice action representation corresponding to 3D Ising's statistical model.

20 pages

References in corpus (2)

• On the solutions to the multi-parametric Yang-Baxter equations
• Simplified tetrahedron equations: Fermionic realization