Integrable perturbations of Ising model
imported>Pythagoras0님의 2013년 2월 24일 (일) 14:52 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.
- http://www.google.com/search?hl=en&tbs=tl:1&q=
- massive integrable perturbations and quasi-particles
- exact S-matrices in ATFT
- Purely Elastic Scattering Theories and Their Ultraviolet Limits
encyclopedia
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.
- Jihye Seo, Solving 2D Magnetic Ising Model at $T=T_c$ Using Scattering Theory 2009
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.
- Alessandro Nigro On the integrable structure of the Ising model J. Stat. Mech. (2008) P01017
- G. Delfinoa and G. Mussardo Non-integrable aspects of the multi-frequency sine-Gordon model, 1998
- G. Delfinoa and G. Mussardo The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T = Tc, 1995
- V. V. Bazhanov, B. Nienhuis, S. O. Warnaar Lattice Ising model in a field: E8 scattering theory, 1994
- [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
- [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]A.B. Zamolodchikov Integrable field theory from conformal field theory, Adv. Stud. Pure Math. 19, 641-674 (1989)
- Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu Ising Field Theory: Quadratic Difference Equations for the n-Point Green's Functions on the Lattice, Phys. Rev. Lett. 46, 757–760 (1981)
- [MTW77]Barry M. McCoy, Craig A. Tracy, Tai Tsun Wu Two-Dimensional Ising Model as an Exactly Solvable Relativistic Quantum Field Theory: Explicit Formulas for n-Point Functions, Phys. Rev. Lett. 38, 793–796 (1977)
- [Kau49] Bruria Kaufman Statistics. II. Partition Function Evaluated by Spinor Analysis, Phys. Rev. 76, 1232–1243 (1949) Crystal
- http://dx.doi.org/10.1038/464362a