Integrable perturbations of Ising model

energy perturbation [Kau49], [MTW77]
- related to A1
- Ising field theory
magnetic perturbation[Zam89]
- related to E8

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
[Zam89]

Soon after Zamolodchikov’s first paper 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. This is the essential role of E8 in the numerical predictions relevant to the cobalt niobate experiment. (In the next section, we will explain how the masses that Zamolodchikov found arise naturally in terms of the algebra structure. But that is just a bonus.)
http://www.google.com/search?hl=en&tbs=tl:1&q=

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.

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
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

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