Free-fermion models and the two-dimensional Ising models under the zero field and imaginary field $i(π/2){k_B}T$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914094301315072 |
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| author | Li, De-Zhang Wang, Xin Yang, Xiao-Bao |
| author_facet | Li, De-Zhang Wang, Xin Yang, Xiao-Bao |
| contents | Ising model is famous in condensed matter and statistical physics. In this work we present a free-fermion formulation of the two-dimensional classical Ising models on the honeycomb, triangular and Kagomé lattices. Each Ising model is studied in the cases of a zero field and of an imaginary field $i(π/2){k_B}T$. We employ the decorated lattice technique, star-triangle transformation and weak-graph expansion method to exactly map each Ising model in both cases into an eight-vertex model on the square lattice. The resulting vertex weights are shown to satisfy the free-fermion condition. In the zero field case, each Ising model is an even free-fermion model. In the case of the imaginary field, the Ising model on the honeycomb lattice is an even free-fermion model while the models on the triangular and Kagomé lattices are odd free-fermion models. We obtain the exact solution of the Kagomé lattice Ising model under the imaginary field $i(π/2){k_B}T$, a result not previously reported in the literature. We also show that the frustrated Ising models on the triangular and Kagomé lattices in the imaginary field still exhibit a non-zero residual entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free-fermion models and the two-dimensional Ising models under the zero field and imaginary field $i(π/2){k_B}T$ Li, De-Zhang Wang, Xin Yang, Xiao-Bao Statistical Mechanics Mathematical Physics Ising model is famous in condensed matter and statistical physics. In this work we present a free-fermion formulation of the two-dimensional classical Ising models on the honeycomb, triangular and Kagomé lattices. Each Ising model is studied in the cases of a zero field and of an imaginary field $i(π/2){k_B}T$. We employ the decorated lattice technique, star-triangle transformation and weak-graph expansion method to exactly map each Ising model in both cases into an eight-vertex model on the square lattice. The resulting vertex weights are shown to satisfy the free-fermion condition. In the zero field case, each Ising model is an even free-fermion model. In the case of the imaginary field, the Ising model on the honeycomb lattice is an even free-fermion model while the models on the triangular and Kagomé lattices are odd free-fermion models. We obtain the exact solution of the Kagomé lattice Ising model under the imaginary field $i(π/2){k_B}T$, a result not previously reported in the literature. We also show that the frustrated Ising models on the triangular and Kagomé lattices in the imaginary field still exhibit a non-zero residual entropy. |
| title | Free-fermion models and the two-dimensional Ising models under the zero field and imaginary field $i(π/2){k_B}T$ |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2406.00232 |