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Anizotropic Ising Model on 2D Kagomé Lattice as an Inhomogeneous XYZ Integrable Model

  • Shahane A. Khachatryan
  • Hrachya Babujian
  • Ara G. Sedrakyan
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Abstract

We investigate a generalized inhomogeneous two-dimensional Ising model on the kagomé lattice with two alternating couplings Ji and J'i, i=1,2,3, along the three lattice directions. The local Boltzmann weights are mapped onto a non-symmetric eight-vertex R-matrix satisfying the free-fermion condition for arbitrary values of the six couplings. We analyze the Yang--Baxter structure for the cases J'i=Ji and J'i=−Ji and derive the corresponding one-dimensional quantum spin chains in the anisotropic limit. The first case yields a transverse-field Ising-type Hamiltonian, while the second leads to a modified chain with a graded permutation structure and shifted partition-function zeros. For a partially anisotropic model, we also obtain the free energy and specific heat.

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Cite

BibTeXRIS
BibTeX
@misc{khachatryan2026anizotropic,
  title = {{Anizotropic Ising Model on 2D Kagomé Lattice as an Inhomogeneous XYZ Integrable Model}},
  author = {Shahane A. Khachatryan and Hrachya Babujian and Ara G. Sedrakyan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.10163},
  eprint = {2609.10163},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.10163},
}
RIS
TY  - UNPB
TI  - Anizotropic Ising Model on 2D Kagomé Lattice as an Inhomogeneous XYZ Integrable Model
AU  - Shahane A. Khachatryan
AU  - Hrachya Babujian
AU  - Ara G. Sedrakyan
PY  - 2026
DA  - 2026/09/09
PB  - arXiv
DO  - 10.48550/arxiv.2609.10163
UR  - https://arxiv.org/abs/2609.10163
AB  - We investigate a generalized inhomogeneous two-dimensional Ising model on the kagomé lattice with two alternating couplings J_i and J'_i, i=1,2,3, along the three lattice directions. The local Boltzmann weights are mapped onto a non-symmetric eight-vertex R-matrix satisfying the free-fermion condition for arbitrary values of the six couplings. We analyze the Yang--Baxter structure for the cases J'_i=J_i and J'_i=−J_i and derive the corresponding one-dimensional quantum spin chains in the anisotropic limit. The first case yields a transverse-field Ising-type Hamiltonian, while the second leads to a modified chain with a graded permutation structure and shifted partition-function zeros. For a partially anisotropic model, we also obtain the free energy and specific heat.
ER  -