"Eight-vertex model and quantum XYZ model"의 두 판 사이의 차이

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==introduction==
 
==introduction==
  
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*  This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases.<br>
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*  This model includes the dimer, ice and zero-field Ising, F and KDP models as special cases.
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*  Sutherland 1970 showed that any eight-vertex model transfer matrix commutes with an XYZ Hamiltonian<br>
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*  Sutherland 1970 showed that any eight-vertex model transfer matrix commutes with an XYZ Hamiltonian
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*  Baxter considered (unaware of Sutherland 1970) the problem of the commutation of two eight-vertex transfer matrices<br>
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*  Baxter considered (unaware of Sutherland 1970) the problem of the commutation of two eight-vertex transfer matrices
  
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==Hamiltonian==
 
==Hamiltonian==
  
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*  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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*  XYZ Hamiltonian
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:<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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==history==
 
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* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
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==related items==
 
==related items==
  
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* [[Heisenberg spin chain model]]<br>
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* [[Heisenberg spin chain model]]
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* [[six-vertex model and Quantum XXZ Hamiltonian]]<br>
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* [[six-vertex model and Quantum XXZ Hamiltonian]]
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* [[Yang-Baxter equation (YBE)|Yang-Baxter equation]]<br>
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* [[Yang-Baxter equation (YBE)|Yang-Baxter equation]]
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* [[dimer model|Dimer model]]<br>
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* [[dimer model|Dimer model]]
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==encyclopedia==
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* http://en.wikipedia.org/wiki/
 
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* http://www.scholarpedia.org/
 
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* http://www.proofwiki.org/wiki/
 
  
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==books==
 
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* [[2010년 books and articles]]<br>
 
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* http://gigapedia.info/1/
 
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* http://gigapedia.info/1/
 
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* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
 
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[[4909919|4909919]]
 
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==articles==
 
==articles==
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* Hjalmar Rosengren, Elliptic pfaffians and solvable lattice models, arXiv:1605.02915 [math-ph], May 10 2016, http://arxiv.org/abs/1605.02915
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* Moll, Alexander. “Random Partitions and the Quantum Benjamin-Ono Hierarchy.” arXiv:1508.03063 [math-Ph, Physics:nlin], August 12, 2015. http://arxiv.org/abs/1508.03063.
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* Rosengren, Hjalmar. “Special Polynomials Related to the Supersymmetric Eight-Vertex Model: A Summary.” arXiv:1503.02833 [math-Ph, Physics:nlin], March 10, 2015. http://arxiv.org/abs/1503.02833.
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* 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.
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* 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/
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* [http://dx.doi.org/10.1006/aphy.2000.6010 Partition Function of the Eight-Vertex Lattice Model]
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**  Baxter, Rodney , J. Publication: Annals of Physics, 70, Issue 1, p.193-228, 1972
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* http://dx.doi.org/10.1063/1.1665111
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**  B. Sutherland, J. Math. Phys. 11:3183-3186 (1970)
  
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* [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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** Atsuo Kuniba, Yasuhiro Akutsu1 and Miki Wadati, 1986
 
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* [http://dx.doi.org/10.1006/aphy.2000.6010 Partition Function of the Eight-Vertex Lattice Model]<br>
 
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**  Baxter, Rodney , J. Publication: Annals of Physics, 70, Issue 1, p.193-228, 1972<br>
 
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* http://dx.doi.org/10.1063/1.1665111<br>
 
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**  B. Sutherland, J. Math. Phys. 11:3183-3186 (1970)<br>
 
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* http://www.ams.org/mathscinet
 
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* [http://www.zentralblatt-math.org/zmath/en/ ]http://www.zentralblatt-math.org/zmath/en/
 
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* http://arxiv.org/
 
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* http://www.pdf-search.org/
 
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* http://pythagoras0.springnote.com/
 
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* [http://math.berkeley.edu/%7Ereb/papers/index.html http://math.berkeley.edu/~reb/papers/index.html]
 
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* http://dx.doi.org/10.1143/JPSJ.55.3285
 
  
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==question and answers(Math Overflow)==
 
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* http://mathoverflow.net/search?q=
 
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* http://mathoverflow.net/search?q=
 
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==blogs==
 
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*  구글 블로그 검색<br>
 
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**  http://blogsearch.google.com/blogsearch?q=<br>
 
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** http://blogsearch.google.com/blogsearch?q=
 
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* http://ncatlab.org/nlab/show/HomePage
 
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==experts on the field==
 
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* http://arxiv.org/
 
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==links==
 
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* [http://detexify.kirelabs.org/classify.html Detexify2 - LaTeX symbol classifier]
 
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* [http://pythagoras0.springnote.com/pages/1947378 수식표현 안내]
 
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* [http://www.research.att.com/%7Enjas/sequences/index.html The On-Line Encyclopedia of Integer Sequences]
 
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* http://functions.wolfram.com/
 
 
[[분류:integrable systems]]
 
[[분류:integrable systems]]
 
[[분류:math and physics]]
 
[[분류:math and physics]]
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[[분류:math and physics]]
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[[분류:migrate]]
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==메타데이터==
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===위키데이터===
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* ID :  [https://www.wikidata.org/wiki/Q5348943 Q5348943]
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===Spacy 패턴 목록===
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* [{'LOWER': 'eight'}, {'OP': '*'}, {'LOWER': 'vertex'}, {'LEMMA': 'model'}]

2021년 2월 17일 (수) 02:08 기준 최신판

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

\[\hat H = -\frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}^z - h\sigma_j^{z})\]



related items




articles

  • Hjalmar Rosengren, Elliptic pfaffians and solvable lattice models, arXiv:1605.02915 [math-ph], May 10 2016, http://arxiv.org/abs/1605.02915
  • Moll, Alexander. “Random Partitions and the Quantum Benjamin-Ono Hierarchy.” arXiv:1508.03063 [math-Ph, Physics:nlin], August 12, 2015. http://arxiv.org/abs/1508.03063.
  • Rosengren, Hjalmar. “Special Polynomials Related to the Supersymmetric Eight-Vertex Model: A Summary.” arXiv:1503.02833 [math-Ph, Physics:nlin], March 10, 2015. http://arxiv.org/abs/1503.02833.
  • 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)

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'eight'}, {'OP': '*'}, {'LOWER': 'vertex'}, {'LEMMA': 'model'}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Eight-vertex_model_and_quantum_XYZ_model&oldid=51692"