"Six-vertex model and Quantum XXZ Hamiltonian"의 두 판 사이의 차이
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<h5>types of six vertex models</h5> | <h5>types of six vertex models</h5> | ||
| − | * | + | * on a square lattice with periodic boundary conditions |
| − | * | + | * on a square lattice with domain wall boundary conditions |
| 105번째 줄: | 105번째 줄: | ||
* [http://arxiv.org/abs/hep-th/9204064 Diagonalization of the XXZ Hamiltonian by Vertex Operators]<br> | * [http://arxiv.org/abs/hep-th/9204064 Diagonalization of the XXZ Hamiltonian by Vertex Operators]<br> | ||
** Authors: Brian Davies, Omar Foda, Michio Jimbo, Tetsuji Miwa, Atsushi Nakayashiki, 1993 | ** Authors: Brian Davies, Omar Foda, Michio Jimbo, Tetsuji Miwa, Atsushi Nakayashiki, 1993 | ||
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| + | E.H. Lieb. <em>Phys. Rev.</em> '''18''' (1967), p. 1046. [http://www.sciencedirect.com/science?_ob=RedirectURL&_method=outwardLink&_partnerName=3&_originPage=article&_zone=art_page&_targetURL=http%3A%2F%2Fdx.doi.org%2F10.1103%252FPhysRevLett.18.1046&_acct=C000059607&_version=1&_userid=4420&md5=d9763691bc80a397c59ec4e9e3ef0891 Full Text via CrossRef]<br> E.H. Lieb. <em>Phys. Rev.</em> '''19''' (1967), p. 108. [http://www.sciencedirect.com/science?_ob=RedirectURL&_method=outwardLink&_partnerName=3&_originPage=article&_zone=art_page&_targetURL=http%3A%2F%2Fdx.doi.org%2F10.1103%252FPhysRevLett.19.108&_acct=C000059607&_version=1&_userid=4420&md5=4e12fda035ad9b1ae9735cb48f90e619 Full Text via CrossRef] | ||
* [[2010년 books and articles|논문정리]] | * [[2010년 books and articles|논문정리]] | ||
2010년 2월 24일 (수) 07:17 판
introduction
- XXZ spin chain and the six-vertex transfer matrix have the same eigenvectors
- Boltzmann weights
- monodromy matrix
- trace of monodromy matrix is the transfer matrix
- power of transfer matrix becomes the partition function
types of six vertex models
- on a square lattice with periodic boundary conditions
- on a square lattice with domain wall boundary conditions
transfer matrix
- finding eigenvalues and eigenvectors of transfer matrix is crucial
- Bethe ansatz equation is used to find the eigenvectors and eigenvalues
partition function
free energy
- \(F=-kT \ln Z\)
correlation functions
books
- Exactly Solved Models in Statistical mechanics
- R. J. Baxter, 1982
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://gigapedia.info/1/
- http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
encyclopedia
- http://ko.wikipedia.org/wiki/
- http://en.wikipedia.org/wiki/http://en.wikipedia.org/wiki/Ice-type_model
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
blogs
- 구글 블로그 검색
articles
- Integrability of the Quantum XXZ Hamiltonian
- T Miwa, 2009
- Introduction to solvable lattice models in statistical and mathematical physics
- Tetsuo Deguchi, 2003
- Diagonalization of the XXZ Hamiltonian by Vertex Operators
- Authors: Brian Davies, Omar Foda, Michio Jimbo, Tetsuji Miwa, Atsushi Nakayashiki, 1993
E.H. Lieb. Phys. Rev. 18 (1967), p. 1046. Full Text via CrossRef
E.H. Lieb. Phys. Rev. 19 (1967), p. 108. Full Text via CrossRef
- 논문정리
- http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4=
- http://www.zentralblatt-math.org/zmath/en/
- http://pythagoras0.springnote.com/
- http://math.berkeley.edu/~reb/papers/index.html
- http://www.ams.org/mathscinet
- http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
- http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
- http://dx.doi.org/