Integrable perturbations of Ising model

introduction

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

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=

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
[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