Eight-vertex model and quantum XYZ model
http://bomber0.myid.net/ (토론)님의 2010년 11월 30일 (화) 10:04 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
\(\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z - h\sigma_j^{z})\)
history
- Heisenberg spin chain model
- six-vertex model and Quantum XXZ Hamiltonian
- Yang-Baxter equation
- Dimer model
encyclopedia
- http://en.wikipedia.org/wiki/
- http://www.scholarpedia.org/
- http://www.proofwiki.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
books
- 2010년 books and articles
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
[[4909919|]]
articles
- Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models
- 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)
- http://www.ams.org/mathscinet
- [1]http://www.zentralblatt-math.org/zmath/en/
- http://arxiv.org/
- http://www.pdf-search.org/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://dx.doi.org/10.1143/JPSJ.55.3285
question and answers(Math Overflow)
blogs
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experts on the field