Integral equations and long-time asymptotics for finite-temperature Ising chain correlation functions

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2008, Issue 3, 2008, Pages

  Doyon, Benjamin ^a   Gamsa, Adam ^b  

^a DURHAM UNIVERSITY   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Classical integrability; Correlation functions; Form factors; Integrable quantum field theory

Indexed keywords

EID: 43149094906     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2008/03/P03012     Document Type: Article

References (34)

1. Altshuler BL, Konik RM and Tsvelik AM 2006 Low temperature correlation functions in integrable models: derivation of the large distance and time asymptotics from the form factor expansion Nucl. Phys. B 739 311 [cond-mat/0508618]
2. Arimitsu T and Umezawa H 1987 Non-equilibrium thermo field dynamics Prog. Theor. Phys. 77 32
3. Arimitsu T and Umezawa H 1987 General structure of non-equilibrium thermo field dynamics Prog. Theor. Phys. 77 53
4. Babelon O and Bernard D 1992 From form factors to correlation functions: the Ising model Phys. Lett. B 288 113 [hep-th/9206003]
5. Babelon O, Bernard D and Talon M 2003 Introduction to Classical Integrable Systems (Cambridge Monographs on Mathematical Physics) (Cambridge: Cambridge University Press)
6. Berg B, Karowski M and Weisz P 1979 Construction of Green's functions from an exact S-matrix Phys. Rev. D 19 2477
7. Bugrij AI 2001 Form factor representation of the correlation function of the two dimensional Ising model on a cylinder Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Fields Theory (NATO Sci. Ser. II Math. Phys. Chem. vol 35) ed S Pakuliak and G von Gehlen (Dordrecht: Kluwer-Academic) pp65-93 [hep-th/0107117]
8. Bugrij A I and Lisovyy O 2003 Spin matrix elements in 2D Ising model on the finite lattice Phys. Lett. A 319 390
9. Chakrabarti BK, Dutta A and Sen P 1996 Quantum Ising Phases and Transitions in Transverse Ising Models (Berlin: Springer)
10. Doyon B 2005 Finite-temperature form factors in the free Majorana theory J. Stat. Mech. P11006 [hep-th/0506105]
11. Doyon B 2007 Finite-temperature form factors: a review SIGMA 3 011 (Contribution to the Proceedings of the O'Raifeartaigh Symposium) [hep-th/0611066]
12. Essler F and Konik R 2007 Finite-temperature lineshapes in gapped quantum spin chains Preprint 0711.2524
13. Faddeev LD and Takhtajan LA 1987 Hamiltonian Methods in the Theory of Solitons (Classics in Mathematics) (Berlin: Springer)
14. Fonseca P and Zamolodchikov AB 2003 Ward identities and integrable differential equations in the Ising field theory Preprint hep-th/0309228
15. Fonseca P and Zamolodchikov AB 2003 Ising field theory in a magnetic field: analytic properties of the free energy J. Stat. Phys. 110 527
16. Henning PA 1995 Thermo field dynamics for quantum fields with continuous mass spectrum Phys. Rep. 253 235
17. Itzykson C and Drouffe J-M 1989 Statistical Field Theory (Cambridge: Cambridge University Press)
18. Kadanoff LP and Ceva H 1971 Determination of an operator algebra for the two-dimensional Ising model Phys. Rev. B 3 3918
19. Leplae L, Umezawa H and Mancini F 1974 Derivation and application of the boson method in superconductivity Phys. Rep. 10 151
20. Lisovyy O 2002 Nonlinear differential equations for the correlation functions of the 2D Ising model on the cylinder Adv. Theor. Math. Phys. 5 909
21. McCoy B M and Wu TT 1973 The Two-Dimensional Ising Model (Cambridge, MA: Harvard University Press)
22. Perk JH H 1980 Equations of motion for the transverse correlations of the one-dimensional XY-model at finite temperature Phys. Rev. A 79 1
23. Pozsgay B and Takcs G 2007 Form factors in finite volume I: form factors bootstrap and truncated conformal space Nucl. Phys. B 788 167 [0706.1445]
24. Pozsgay B and Takcs G 2007 Form factors in finite volume II: disconnected terms and finite temperature correlators Nucl. Phys. B 788 209 [0706.3605]
25. Reyes SA and Tsvelik AM 2006 Finite temperature correlation function of one-dimensional Quantum Ising model: the virial expansion Phys. Rev. B 73 220405(R) [cond-mat/0605040]
26. Sachdev S 1996 Universal, finite temperature, crossover functions of the quantum transition in the Ising chain in a transverse field Nucl. Phys. B 464 576 [cond-mat/9509147]
27. Sachdev S and Young AP 1997 Low temperature relaxational dynamics of the Ising chain in a transverse field Phys. Rev. Lett. 78 2220 [cond-mat/9609185]
28. Sato M, Miwa T and Jimbo M 1978 Holonomic quantum fields Publ. RIMS Kyoto Univ. 14 223
29. Sato M, Miwa T and Jimbo M 1979 Publ. RIMS Kyoto Univ. 15 201
30. Sato M, Miwa T and Jimbo M 1979 Publ. RIMS Kyoto Univ. 15 577
31. Sato M, Miwa T and Jimbo M 1979 Publ. RIMS Kyoto Univ. 15 871
32. Sato M, Miwa T and Jimbo M 1980 Publ. RIMS Kyoto Univ. 16 531
33. von Gehlen G, Iorgov N, Pakuliak S, Shadura V and Tykhyy Yu 2007 Form-factors in the Baxter-Bazhanov-Stroganov model II: Ising model on the finite lattice Preprint 0711.0457
34. Wu TT, McCoy B M, Tracy CA and Barouch E 1976 Spin-spin correlation functions for the two-dimensional Ising model: exact theory in the scaling region Phys. Rev. B 13 316