A Free-fermion Formulation of Two-dimensional Ising Models
| Autor: | Li, De-Zhang, Wang, Xin, Yang, Xiao-Bao |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Ising model is a famous toy model 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 Kagom\'e lattices. Each Ising model is studied in the case of a zero field and the case of an imaginary field i({\pi}/2)k_BT. 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 those on the triangular and Kagom\'e lattices are odd free-fermion models. The exact solution of the Kagom\'e lattice Ising model in the imaginary field i({\pi}/2)k_BT is obtained, which has not been reported in previous works. The frustrated Ising models on the triangular and Kagom\'e lattices in the imaginary field still exhibit a non-zero residual entropy. Comment: 11 pages, 6 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|