"Eight-vertex model and quantum XYZ model"의 두 판 사이의 차이
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==introduction== | ==introduction== | ||
| − | * This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases. | + | * This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases. |
| − | * Sutherland 1970 showed that any eight-vertex model transfer matrix commutes with an XYZ Hamiltonian | + | * Sutherland 1970 showed that any eight-vertex model transfer matrix commutes with an XYZ Hamiltonian |
| − | * Baxter considered (unaware of | + | * Baxter considered (unaware of Sutherland 1970) the problem of the commutation of two eight-vertex transfer matrices |
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==Hamiltonian== | ==Hamiltonian== | ||
| − | * XYZ Hamiltonian | + | * XYZ Hamiltonian |
| − | + | :<math>\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z - h\sigma_j^{z})</math> | |
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==related items== | ==related items== | ||
| − | * [[Heisenberg spin chain model]] | + | * [[Heisenberg spin chain model]] |
| − | * [[six-vertex model and Quantum XXZ Hamiltonian]] | + | * [[six-vertex model and Quantum XXZ Hamiltonian]] |
| − | * [[Yang-Baxter equation (YBE)|Yang-Baxter equation]] | + | * [[Yang-Baxter equation (YBE)|Yang-Baxter equation]] |
| − | * [[dimer model|Dimer model]] | + | * [[dimer model|Dimer model]] |
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==articles== | ==articles== | ||
| + | * Kuniba, Atsuo, Yasuhiro Akutsu, and Miki Wadati. 1986. “Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models.” Journal of the Physical Society of Japan 55 (10): 3285–3288. doi:10.1143/JPSJ.55.3285. | ||
| + | * Andrews, George E., R. J. Baxter, and P. J. Forrester. 1984. “Eight-vertex SOS Model and Generalized Rogers-Ramanujan-type Identities.” Journal of Statistical Physics 35 (3-4) (May 1): 193–266. doi:10.1007/BF01014383. http://www.springerlink.com/content/r522x4086p54u438/ | ||
| + | * [http://dx.doi.org/10.1006/aphy.2000.6010 Partition Function of the Eight-Vertex Lattice Model] | ||
| + | ** Baxter, Rodney , J. Publication: Annals of Physics, 70, Issue 1, p.193-228, 1972 | ||
| + | * http://dx.doi.org/10.1063/1.1665111 | ||
| + | ** B. Sutherland, J. Math. Phys. 11:3183-3186 (1970) | ||
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[[분류:integrable systems]] | [[분류:integrable systems]] | ||
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[[분류:math and physics]] | [[분류:math and physics]] | ||
2013년 12월 21일 (토) 11:25 판
introduction
- This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases.
- Sutherland 1970 showed that any eight-vertex model transfer matrix commutes with an XYZ Hamiltonian
- Baxter considered (unaware of Sutherland 1970) the problem of the commutation of two eight-vertex transfer matrices
Hamiltonian
- XYZ Hamiltonian
\[\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z - h\sigma_j^{z})\]
- Heisenberg spin chain model
- six-vertex model and Quantum XXZ Hamiltonian
- Yang-Baxter equation
- Dimer model
articles
- Kuniba, Atsuo, Yasuhiro Akutsu, and Miki Wadati. 1986. “Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models.” Journal of the Physical Society of Japan 55 (10): 3285–3288. doi:10.1143/JPSJ.55.3285.
- Andrews, George E., R. J. Baxter, and P. J. Forrester. 1984. “Eight-vertex SOS Model and Generalized Rogers-Ramanujan-type Identities.” Journal of Statistical Physics 35 (3-4) (May 1): 193–266. doi:10.1007/BF01014383. http://www.springerlink.com/content/r522x4086p54u438/
- Partition Function of the Eight-Vertex Lattice Model
- Baxter, Rodney , J. Publication: Annals of Physics, 70, Issue 1, p.193-228, 1972
- http://dx.doi.org/10.1063/1.1665111
- B. Sutherland, J. Math. Phys. 11:3183-3186 (1970)