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 N4 dimensional space VN⊗VN⊗VN⊗VN, appropriate for consideration by means of the cu...

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Bibliographic Details
Published in:Annals of physics 2022-02, Vol.437, p.168735, Article 168735
Main Authors: Khachatryan, Sh, Sedrakyan, A.
Format: Article
Language:English
Subjects:
3D Integrability
Ising model
Potts model
R-matrix
Statistical Physics
Transfer Matrix
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Summary: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.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2021.168735