Eight-vertex model and quantum XYZ model
imported>Pythagoras0님의 2012년 11월 1일 (목) 13:09 판 (찾아 바꾸기 – “* Princeton companion to mathematics(Companion_to_Mathematics.pdf)” 문자열을 “” 문자열로)
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
\(\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z - h\sigma_j^{z})\)
history
- Heisenberg spin chain model
- six-vertex model and Quantum XXZ Hamiltonian
- Yang-Baxter equation
- Dimer model
encyclopedia
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
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articles
- Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models
- Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986
- Partition Function of the Eight-Vertex Lattice Model
- Baxter, Rodney , J. Publication: Annals of Physics, 70, Issue 1, p.193-228, 1972
- 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)
- B. Sutherland, J. Math. Phys. 11:3183-3186 (1970)
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- [1]http://www.zentralblatt-math.org/zmath/en/
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