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

TL;DR

This paper constructs an explicit spectral parameter dependent R-matrix for inhomogeneous 3D chiral Potts models, facilitating integrability analysis and connecting to Bethe ansatz and fermionic lattice actions.

Contribution

It provides the first explicit R-matrix for these models and links the 3D chiral Potts models to 2D quantum spin Hamiltonians and fermionic lattice actions.

Findings

Constructed the spectral parameter dependent R-matrix for 3D chiral Potts models.

Presented 2D quantum spin Hamiltonians for the general case.

Derived a fermionic lattice action for the 3D Ising model at N=2.

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.