"Integrable perturbations of Ising model"의 두 판 사이의 차이
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encyclopedia==
imported>Pythagoras0 잔글 (찾아 바꾸기 – “<h5>” 문자열을 “==” 문자열로) |
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| − | ==introduction | + | ==introduction== |
* energy perturbation '''[Kau49]''', '''[MTW77]'''<br> | * energy perturbation '''[Kau49]''', '''[MTW77]'''<br> | ||
| 11번째 줄: | 11번째 줄: | ||
| − | ==Ising field theory | + | ==Ising field theory== |
* the continuum limit of the Ising model is made to look like a field theory only through the application of a certain transformation (Jordan-Winger)<br> | * the continuum limit of the Ising model is made to look like a field theory only through the application of a certain transformation (Jordan-Winger)<br> | ||
| 22번째 줄: | 22번째 줄: | ||
| − | ==history | + | ==history== |
* Soon after Zamolodchikov’s first paper '''[Zam]''' appeared, | * Soon after Zamolodchikov’s first paper '''[Zam]''' appeared, | ||
| 39번째 줄: | 39번째 줄: | ||
| − | ==related items | + | ==related items== |
* [[massive integrable perturbations of CFT and quasi-particles|massive integrable perturbations and quasi-particles]] | * [[massive integrable perturbations of CFT and quasi-particles|massive integrable perturbations and quasi-particles]] | ||
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| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">encyclopedia== |
* http://en.wikipedia.org/wiki/ | * http://en.wikipedia.org/wiki/ | ||
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| − | ==books | + | ==books== |
| 70번째 줄: | 70번째 줄: | ||
| − | ==expositions | + | ==expositions== |
* David Borthwick and Skip Garibaldi, “Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?,” 1012.5407 (December 24, 2010), http://arxiv.org/abs/1012.5407. | * David Borthwick and Skip Garibaldi, “Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?,” 1012.5407 (December 24, 2010), http://arxiv.org/abs/1012.5407. | ||
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| − | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles | + | <h5 style="line-height: 3.428em; margin: 0px; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">articles== |
* Coldea, R., D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer. 2010. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science 327, no. 5962 (January 8): 177 -180. doi:[http://dx.doi.org/10.1126/science.1180085 10.1126/science.1180085]. | * Coldea, R., D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer. 2010. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science 327, no. 5962 (January 8): 177 -180. doi:[http://dx.doi.org/10.1126/science.1180085 10.1126/science.1180085]. | ||
| 115번째 줄: | 115번째 줄: | ||
| − | ==question and answers(Math Overflow) | + | ==question and answers(Math Overflow)== |
* http://mathoverflow.net/questions/32315/has-the-lie-group-e8-really-been-detected-experimentally | * http://mathoverflow.net/questions/32315/has-the-lie-group-e8-really-been-detected-experimentally | ||
| 126번째 줄: | 126번째 줄: | ||
| − | ==blogs | + | ==blogs== |
* 구글 블로그 검색<br> | * 구글 블로그 검색<br> | ||
| 137번째 줄: | 137번째 줄: | ||
| − | ==experts on the field | + | ==experts on the field== |
* http://arxiv.org/ | * http://arxiv.org/ | ||
| 145번째 줄: | 145번째 줄: | ||
| − | ==links | + | ==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) 15:29 판
introduction
- energy perturbation [Kau49], [MTW77]
- related to A1
- Ising field theory
- magnetic perturbation[Zam89]
- related to E8
Ising field theory
- the continuum limit of the Ising model is made to look like a field theory only through the application of a certain transformation (Jordan-Winger)
- "kink" states (boundaries between regions of differing spin) = basic objects of the theory
- called quasiparticle
history
- Soon after Zamolodchikov’s first paper [Zam] appeared,
- Fateev and Zamolodchikov conjectured in [FZ90] that
- if you take a minimal model CFT constructed from a compact Lie algebra g via the coset construction and perturb it in a particular way, then you obtain the affine Toda field theory (ATFT) associated with g, which is an integrable field theory.
- This was confirmed in [EY] and [HoM].
- If you do this with g = E8, you arrive at the conjectured integrable field theory investigated by Zamolodchikov and described in the previous paragraph.
- That is, if we take the E8 ATFT as a starting point, then the assumptions (Z1)–(Z4) become deductions.
- [EY]T. Eguchi and S.-K. Yang, Deformations of conformal field theories and soliton equations, Phys. Lett. B 224 (1989), 373-8 B
- [HoM]T.J. Hollowood and P.Mansfield, Rational conformal theories at, and away from criticality as Toda field theories, Phys. Lett. B226 (1989) 73-79
- http://www.google.com/search?hl=en&tbs=tl:1&q=
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=
expositions
- David Borthwick and Skip Garibaldi, “Did a 1-dimensional magnet detect a 248-dimensional Lie algebra?,” 1012.5407 (December 24, 2010), http://arxiv.org/abs/1012.5407.
- Affleck, Ian. 2010. “Solid-state physics: Golden ratio seen in a magnet”. Nature 464 (7287) (3월 18): 362-363. doi:10.1038/464362a.
articles==
- Coldea, R., D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer. 2010. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science 327, no. 5962 (January 8): 177 -180. doi:10.1126/science.1180085.
- On the integrable structure of the Ising model
- Alessandro Nigro J. Stat. Mech. (2008) P01017
- Non-integrable aspects of the multi-frequency sine-Gordon model
- G. Delfinoa and G. Mussardo, 1998
- The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc
- G. Delfinoa and G. Mussardo, 1995
- Lattice Ising model in a field: E8 scattering theory
- V. V. Bazhanov, B. Nienhuis, S. O. Warnaar, 1994
- [Zam]INTEGRALS OF MOTION AND S-MATRIX OF THE (SCALED) T = Tc ISING MODEL WITH MAGNETIC FIELD
- [FZ90]V. A. Fateev and A. B. Zamolodchikov. Conformal field theory and purely elastic S-matrices. Int. J. Mod. Phys., A5 (6): 1025-1048
- [Zam89]Integrable field theory from conformal field theory
- A.B. Zamolodchikov, Adv. Stud. Pure Math. 19, 641-674 (1989)
- Ising Field Theory: Quadratic Difference Equations for the n-Point Green's Functions on the Lattice
- Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 46, 757–760 (1981)
- [MTW77]Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions
- Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 38, 793–796 (1977)
- [Kau49]Statistics. II. Partition Function Evaluated by Spinor Analysis
- Bruria Kaufman, Phys. Rev. 76, 1232–1243 (1949) Crystal
- http://www.ams.org/mathscinet
- 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/10.1038/464362a
question and answers(Math Overflow)
- http://mathoverflow.net/questions/32315/has-the-lie-group-e8-really-been-detected-experimentally
- http://mathoverflow.net/questions/32432/does-the-quantum-subgroup-of-quantum-su-2-called-e-8-have-anything-at-all-to-do-w
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field
links
- Coldea, R., D. A. Tennant, E. M. Wheeler, E. Wawrzynska, D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, and K. Kiefer. 2010. Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry. Science 327, no. 5962 (January 8): 177 -180. doi:10.1126/science.1180085.
- On the integrable structure of the Ising model
- Alessandro Nigro J. Stat. Mech. (2008) P01017
- Non-integrable aspects of the multi-frequency sine-Gordon model
- G. Delfinoa and G. Mussardo, 1998
- The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc
- G. Delfinoa and G. Mussardo, 1995
- Lattice Ising model in a field: E8 scattering theory
- V. V. Bazhanov, B. Nienhuis, S. O. Warnaar, 1994
- [Zam]INTEGRALS OF MOTION AND S-MATRIX OF THE (SCALED) T = Tc ISING MODEL WITH MAGNETIC FIELD
- [FZ90]V. A. Fateev and A. B. Zamolodchikov. Conformal field theory and purely elastic S-matrices. Int. J. Mod. Phys., A5 (6): 1025-1048
- [Zam89]Integrable field theory from conformal field theory
- A.B. Zamolodchikov, Adv. Stud. Pure Math. 19, 641-674 (1989)
- Ising Field Theory: Quadratic Difference Equations for the n-Point Green's Functions on the Lattice
- Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 46, 757–760 (1981)
- [MTW77]Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions
- Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 38, 793–796 (1977)
- [Kau49]Statistics. II. Partition Function Evaluated by Spinor Analysis
- Bruria Kaufman, Phys. Rev. 76, 1232–1243 (1949) Crystal
- http://www.ams.org/mathscinet
- 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/10.1038/464362a
question and answers(Math Overflow)
- http://mathoverflow.net/questions/32315/has-the-lie-group-e8-really-been-detected-experimentally
- http://mathoverflow.net/questions/32432/does-the-quantum-subgroup-of-quantum-su-2-called-e-8-have-anything-at-all-to-do-w
- http://mathoverflow.net/search?q=
- http://mathoverflow.net/search?q=
blogs
- 구글 블로그 검색
- http://ncatlab.org/nlab/show/HomePage
experts on the field