"Integrable perturbations of Ising model"의 두 판 사이의 차이

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imported>Pythagoras0
1번째 줄: 1번째 줄:
 
==introduction==
 
==introduction==
  
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*  energy perturbation '''[Kau49]''', '''[MTW77]'''<br>
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*  energy perturbation '''[Kau49]''', '''[MTW77]'''
 
** related to A1
 
** related to A1
 
** Ising field theory
 
** Ising field theory
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*  magnetic perturbation'''[Zam89]'''<br>
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*  magnetic perturbation'''[Zam89]'''
 
** related to E8
 
** related to E8
  
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==Ising field theory==
 
==Ising field theory==
  
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*  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)
 
** "kink" states (boundaries between regions of differing spin) = basic objects of the theory
 
** "kink" states (boundaries between regions of differing spin) = basic objects of the theory
 
** called quasiparticle
 
** called quasiparticle
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*  
 
  
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==history==
 
==history==
  
 
* Soon after Zamolodchikov’s first paper '''[Zam]''' appeared,
 
* Soon after Zamolodchikov’s first paper '''[Zam]''' appeared,
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*  Fateev and Zamolodchikov conjectured in [FZ90] that<br>
+
*  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.
 
** 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].
+
** 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.
 
* 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.
 
* 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
+
* '''[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
+
* '''[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=
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
  
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==related items==
 
==related items==
44번째 줄: 38번째 줄:
 
* [[exact S-matrices in ATFT]]
 
* [[exact S-matrices in ATFT]]
  
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==encyclopedia==
 
==encyclopedia==
55번째 줄: 49번째 줄:
  
  
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==books==
 
==books==
  
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* [[2010년 books and articles]]<br>
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* [[2010년 books and articles]]
 
* 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=
 
* http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=
  
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+
  
 
==expositions==
 
==expositions==
  
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* 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.  
−
*  Affleck, Ian. 2010. “Solid-state physics: Golden ratio seen in a magnet”. <em>Nature</em> 464 (7287) (3월 18): 362-363. doi:[http://dx.doi.org/10.1038/464362a 10.1038/464362a].<br>
+
*  Affleck, Ian. 2010. “Solid-state physics: Golden ratio seen in a magnet”. <em>Nature</em> 464 (7287) (3월 18): 362-363. doi:[http://dx.doi.org/10.1038/464362a 10.1038/464362a].
  
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==articles==
 
==articles==
  
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* 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]. 
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* 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].  
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* [http://dx.doi.org/10.1088/1742-5468/2008/01/P01017 On the integrable structure of the Ising model]<br>
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* [http://dx.doi.org/10.1088/1742-5468/2008/01/P01017 On the integrable structure of the Ising model]
 
** Alessandro Nigro J. Stat. Mech. (2008) P01017
 
** Alessandro Nigro J. Stat. Mech. (2008) P01017
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* [http://dx.doi.org/10.1016/S0550-3213%2898%2900063-7 Non-integrable aspects of the multi-frequency sine-Gordon model]<br>
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* [http://dx.doi.org/10.1016/S0550-3213%2898%2900063-7 Non-integrable aspects of the multi-frequency sine-Gordon model]
 
** G. Delfinoa and G. Mussardo, 1998
 
** G. Delfinoa and G. Mussardo, 1998
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* [http://dx.doi.org/10.1016/0550-3213%2895%2900464-4 The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc]<br>
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* [http://dx.doi.org/10.1016/0550-3213%2895%2900464-4 The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc]
 
** G. Delfinoa and G. Mussardo, 1995
 
** G. Delfinoa and G. Mussardo, 1995
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* [http://dx.doi.org/10.1016/0370-2693%2894%2991107-X Lattice Ising model in a field: E8 scattering theory]<br>
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* [http://dx.doi.org/10.1016/0370-2693%2894%2991107-X Lattice Ising model in a field: E8 scattering theory]
 
** V. V. Bazhanov, B. Nienhuis, S. O. Warnaar, 1994
 
** V. V. Bazhanov, B. Nienhuis, S. O. Warnaar, 1994
 
* '''[Zam]'''[http://dx.doi.org/10.1142/S0217751X8900176X INTEGRALS OF MOTION AND S-MATRIX OF THE (SCALED) T = Tc ISING MODEL WITH MAGNETIC FIELD]
 
* '''[Zam]'''[http://dx.doi.org/10.1142/S0217751X8900176X 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
 
* '''[FZ90]'''V. A. Fateev and A. B. Zamolodchikov. Conformal field theory and purely elastic S-matrices. Int. J. Mod. Phys., A5 (6): 1025-1048
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* '''[Zam89]'''Integrable field theory from conformal field theory<br>
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* '''[Zam89]'''Integrable field theory from conformal field theory
 
** A.B. Zamolodchikov, Adv. Stud. Pure Math. 19, 641-674 (1989)
 
** A.B. Zamolodchikov, Adv. Stud. Pure Math. 19, 641-674 (1989)
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* [http://dx.doi.org/10.1103/PhysRevLett.46.757 Ising Field Theory: Quadratic Difference Equations for the n-Point Green's Functions on the Lattice]<br>
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* [http://dx.doi.org/10.1103/PhysRevLett.46.757 Ising Field Theory: Quadratic Difference Equations for the n-Point Green's Functions on the Lattice]
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** Barry M. McCoy,  Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 46, 757–760 (1981)
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** Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 46, 757–760 (1981)
  
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* '''[MTW77]'''[http://dx.doi.org/10.1103/PhysRevLett.38.793 Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions]<br>
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* '''[MTW77]'''[http://dx.doi.org/10.1103/PhysRevLett.38.793 Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions]
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** Barry M. McCoy,  Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 38, 793–796 (1977)
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** Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu, Phys. Rev. Lett. 38, 793–796 (1977)
  
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* '''[Kau49]'''[http://dx.doi.org/10.1103/PhysRev.76.1232 Statistics. II. Partition Function Evaluated by Spinor Analysis]<br>
+
* '''[Kau49]'''[http://dx.doi.org/10.1103/PhysRev.76.1232 Statistics. II. Partition Function Evaluated by Spinor Analysis]
 
** Bruria Kaufman, Phys. Rev. 76, 1232–1243 (1949) Crystal
 
** Bruria Kaufman, Phys. Rev. 76, 1232–1243 (1949) Crystal
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* http://www.ams.org/mathscinet
 
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* 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]
 
 
* http://dx.doi.org/10.1038/464362a
 
* http://dx.doi.org/10.1038/464362a
  
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==question and answers(Math Overflow)==
 
==question and answers(Math Overflow)==
119번째 줄: 106번째 줄:
 
* 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
 
* 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/questions/32432/does-the-quantum-subgroup-of-quantum-su-2-called-e-8-have-anything-at-all-to-do-w
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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]]
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[[분류:math and physics]]
 
 
[[분류:math and physics]]
 
[[분류:math and physics]]

2013년 2월 24일 (일) 12:28 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=



related items



encyclopedia




books


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



question and answers(Math Overflow)

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