"Eight-vertex model and quantum XYZ model"의 두 판 사이의 차이
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| − | + | ==introduction== | |
* This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases.<br> | * This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases.<br> | ||
| 11번째 줄: | 11번째 줄: | ||
| − | + | ==Hamiltonian== | |
* XYZ Hamiltonian<br><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><br> | * XYZ Hamiltonian<br><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><br> | ||
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| − | + | ==history== | |
* http://www.google.com/search?hl=en&tbs=tl:1&q= | * http://www.google.com/search?hl=en&tbs=tl:1&q= | ||
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| − | + | ==related items== | |
* [[Heisenberg spin chain model]]<br> | * [[Heisenberg spin chain model]]<br> | ||
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| − | + | ==encyclopedia== | |
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
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| − | + | ==books== | |
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| − | + | ==articles== | |
* [http://dx.doi.org/10.1143/JPSJ.55.3285 Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models]<br> | * [http://dx.doi.org/10.1143/JPSJ.55.3285 Virasoro Algebra, von Neumann Algebra and Critical Eight-Vertex SOS Models]<br> | ||
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| − | + | ==question and answers(Math Overflow)== | |
* http://mathoverflow.net/search?q= | * http://mathoverflow.net/search?q= | ||
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| − | + | ==blogs== | |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
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| − | + | ==experts on the field== | |
* http://arxiv.org/ | * http://arxiv.org/ | ||
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| − | + | ==links== | |
* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | * [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier] | ||
2012년 10월 28일 (일) 16:16 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=
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)
- 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
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field