"Six-vertex model and Quantum XXZ Hamiltonian"의 두 판 사이의 차이
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| 1번째 줄: | 1번째 줄: | ||
<h5>introduction</h5> | <h5>introduction</h5> | ||
| + | * ice-type model, R model, Rys model | ||
* XXZ spin chain and the six-vertex transfer matrix have the same eigenvectors | * XXZ spin chain and the six-vertex transfer matrix have the same eigenvectors | ||
| 133번째 줄: | 134번째 줄: | ||
* [http://www.springerlink.com/content/f9961j132852j27q/ Integrability of the Quantum XXZ Hamiltonian]<br> | * [http://www.springerlink.com/content/f9961j132852j27q/ Integrability of the Quantum XXZ Hamiltonian]<br> | ||
** T Miwa, 2009 | ** T Miwa, 2009 | ||
| − | |||
* [http://arxiv.org/abs/cond-mat/0304309 Introduction to solvable lattice models in statistical and mathematical physics]<br> | * [http://arxiv.org/abs/cond-mat/0304309 Introduction to solvable lattice models in statistical and mathematical physics]<br> | ||
** Tetsuo Deguchi, 2003 | ** Tetsuo Deguchi, 2003 | ||
* [http://front.math.ucdavis.edu/0010.6421 Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta = {1/2}$]<br> | * [http://front.math.ucdavis.edu/0010.6421 Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta = {1/2}$]<br> | ||
** V. Fridkin, Yu. Stroganov, D. Zagier, 2000 | ** V. Fridkin, Yu. Stroganov, D. Zagier, 2000 | ||
| − | |||
* [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 | ||
| 149번째 줄: | 148번째 줄: | ||
** B. Sutherland. <em style="line-height: 2em;">Phys. Rev.</em> '''19''' (1967), p. 103. [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.19.103&_acct=C000059607&_version=1&_userid=4420&md5=bbeb93e683f2654b0eadeaa7cbd82f5c Full Text via CrossRef] | ** B. Sutherland. <em style="line-height: 2em;">Phys. Rev.</em> '''19''' (1967), p. 103. [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.19.103&_acct=C000059607&_version=1&_userid=4420&md5=bbeb93e683f2654b0eadeaa7cbd82f5c Full Text via CrossRef] | ||
* One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System<br> | * One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System<br> | ||
| − | ** | + | ** C. N. Yang, C. P. Yang, 1966 |
| + | * One-dimensional chain of anisotropic spin-spin interactions<br> | ||
| + | ** C. N. Yang, C. P. Yang, 1966 | ||
* [[2010년 books and articles|논문정리]] | * [[2010년 books and articles|논문정리]] | ||
* http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4= | * http://www.ams.org/mathscinet/search/publications.html?pg4=ALLF&s4= | ||
2010년 3월 27일 (토) 10:51 판
introduction
- ice-type model, R model, Rys model
- 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
- this is related to the Alternating sign matrix theorem
transfer matrix
- finding eigenvalues and eigenvectors of transfer matrix is crucial
- Bethe ansatz equation is used to find the eigenvectors and eigenvalues
anistropic one-dimensional Heisenberg model
- Heisenberg model
- XXZ model or XXZ spin chain
- first solved by Bethe
- Yang and Yang
- ground state eigevector for Hamiltonian is a common eigenvector
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/Ice-type_model
- http://en.wikipedia.org/wiki/Heisenberg_model_(quantum)
- http://en.wikipedia.org/wiki/
- Princeton companion to mathematics(Companion_to_Mathematics.pdf)
blogs
- 구글 블로그 검색
STATISTICAL MECHANICS-A REVIEW OF
SELECTED RIGOROUS RESULTS1•2
By JOEL L. LEBOWITZ
Method for calculating finite size corrections in Bethe ansatz systems: Heisenberg chain and six-vertex model
de Vega, H. J.; Woynarovich, F.
articles
- Integrability of the Quantum XXZ Hamiltonian
- T Miwa, 2009
- Introduction to solvable lattice models in statistical and mathematical physics
- Tetsuo Deguchi, 2003
- Finite Size XXZ Spin Chain with Anisotropy Parameter $\Delta = {1/2}$
- V. Fridkin, Yu. Stroganov, D. Zagier, 2000
- 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. Letters18, 692 (1967)
- Exact Solution of the F Model of An Antiferroelectric
- E.H. Lieb. Phys. Rev. 18 (1967), p. 1046. Full Text via CrossRef
- Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric
- E.H. Lieb. Phys. Rev. 19 (1967), p. 108. Full Text via CrossRef
- Exact Solution of a Two-Dimensional Model for Hydrogen-Bonded Crystals
- B. Sutherland. Phys. Rev. 19 (1967), p. 103. Full Text via CrossRef
- One-Dimensional Chain of Anisotropic Spin-Spin Interactions. II. Properties of the Ground-State Energy Per Lattice Site for an Infinite System
- C. N. Yang, C. P. Yang, 1966
- One-dimensional chain of anisotropic spin-spin interactions
- C. N. Yang, C. P. Yang, 1966
- 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/