Ising Model in a Magnetic Field

The Quantum Field Theory Approach to the Calculation of the Spin-Spin Correlation Function
  • G. Delfino
  • G. Mussardo
Part of the NATO ASI Series book series (NSSB, volume 361)

Abstract

The calculation of the spin-spin correlation function G(x) =< σ(x)σ(0) > of the two-dimensional Ising Model in a magnetic field has been a long-standing problem of statistical mechanics. Solution of this problem has been recently obtained by using a quantum field theory approach based on the spectral representation method for correlation functions [1]. The aim of this talk is to illustrate in a plain language the main features of the solution and to comment on some interesting aspects of the method we used.

Keywords

Exter 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    G. Delfino and G. Mussardo, Nucl. Phys. B455 (1995), 724.MathSciNetADSCrossRefMATHGoogle Scholar
  2. [2]
    A.A. Belavin, A.M. Polyakov and A.B. Zamolodchikov, Nucl. Phys. B 241 (1984), 333.MathSciNetADSCrossRefMATHGoogle Scholar
  3. [3]
    A.B. Zamolodchikov, in Advanced Studies in Pure Mathematics 19 (1989), 641MathSciNetGoogle Scholar
  4. [3]
    A.B. Zamolodchikov, Int. J. Mod. Phys. A 3 (1988), 743.MathSciNetADSCrossRefGoogle Scholar
  5. [4]
    V.A. Fateev and A.B. Zamolodchikov, Int. J. Mod. Phys. A 5 (1990), 1025.MathSciNetADSCrossRefGoogle Scholar
  6. [5]
    B. Berg, M. Karowski, P. Weisz, Phys. Rev. D 19 (1979), 2477;ADSGoogle Scholar
  7. [5]
    M. Karowski, P. Weisz, Nucl. Phys. B 139 (1978), 445;MathSciNetADSCrossRefGoogle Scholar
  8. [5]
    M. Karowski, Phys. Rep. 49 (1979), 229;ADSCrossRefGoogle Scholar
  9. [6]
    F.A. Smirnov, Form Factors in Completely Integrable Models of Quantum Field Theory (World Scientific) 1992, and references therein.CrossRefMATHGoogle Scholar
  10. [7]
    J.L. Cardy and G. Mussardo, Nucl. Phys. B410 [FS] (1993), 451.MathSciNetADSCrossRefMATHGoogle Scholar
  11. [8]
    V.P. Yurov and Al.B. Zamolodchikov, Int. J. Mod. Phys. A 6 (1991), 3419.MathSciNetADSCrossRefGoogle Scholar
  12. [9]
    J.L. Cardy and G. Mussardo, Nucl. Phys. B340 (1990), 387.MathSciNetADSCrossRefGoogle Scholar
  13. [10]
    A.B. Zamolodchikov, Nucl. Phys. B348 (1991), 619.MathSciNetADSCrossRefGoogle Scholar
  14. [11]
    G. Delfino and G. Mussardo, Phys. Lett.B 324 (1994), 40;MathSciNetADSCrossRefGoogle Scholar
  15. [11]
    J. Balog, Phys. Lett. B300 (1993), 145.CrossRefGoogle Scholar
  16. [12]
    A. Fring, G. Mussardo and P. Simonetti, Nucl. Phys. B393 (1993), 413;MathSciNetADSCrossRefMATHGoogle Scholar
  17. [12]
    G. Mussardo and P. Simonetti, Int. J. Mod. Phys. A9 (1994), 3307.MathSciNetADSCrossRefMATHGoogle Scholar
  18. [13]
    G. Delfino, G. Mussardo and P. Simonetti, Phys. Rev. D51 (1995), 6620.ADSGoogle Scholar
  19. [14]
    T.T. Wu, B.M. McCoy, C.A. Tracy and E. Barouch, Phys. Rev. B13 (1978), 316.CrossRefGoogle Scholar
  20. [15]
    B.M. McCoy and T.T. Wu, The Two-Dimensional Ising Model (Harvard University Press, Cambridge, 1973).MATHGoogle Scholar
  21. [16]
    B.M. McCoy, C.A. Tracy and T.T. Wu, Jour. Math. Phys. 18 (1977), 1058.MathSciNetADSCrossRefMATHGoogle Scholar
  22. [17]
    M. Sato, T. Miwa and M. Jimbo, Publ. RIMS, Kyoto Univ. 14 (1978), 223.MathSciNetCrossRefMATHGoogle Scholar
  23. [18]
    J. Palmer and C.A. Tracy, Adv. in Applied Math. 2 (1981) 329;MathSciNetCrossRefMATHGoogle Scholar
  24. [19]
    O. Babelon and D. Bernard, Phys. Lett. B288 (1992), 113.MathSciNetCrossRefGoogle Scholar
  25. [20]
    S. Coleman and H.J. Thun, Commun. Math. Phys. 61 (1978), 31;MathSciNetADSCrossRefGoogle Scholar
  26. [20]
    C.J. Goebel, Prog. Theor. Phys. Supplement 86 (1986), 261.ADSCrossRefGoogle Scholar
  27. [21]
    H.W. Braden, E. Corrigan, P.E. Dorey and R. Sasaki, Nucl. Phys. B338 (1990), 689;MathSciNetADSCrossRefMATHGoogle Scholar
  28. [21]
    H.W. Braden, E. Corrigan, P.E. Dorey and R. Sasaki, Nucl. Phys. B356 (1991), 469.MathSciNetADSCrossRefGoogle Scholar
  29. [22]
    P. Christe and G. Mussardo, Nucl. Phys. B330 (1990), 465;MathSciNetADSCrossRefGoogle Scholar
  30. [22]
    P. Christe and G. Mussardo, Int. J. Mod. Phys. A5 (1990), 4581.MathSciNetADSCrossRefGoogle Scholar
  31. [23]
    P.G. Lauwers and V. Rittenberg, Numerical Estimates of the Spin-Spin Correlation Function for the Critical 2-D Ising Model in a Magnetic Field, Bonn-HE-89–11.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • G. Delfino
    • 1
  • G. Mussardo
    • 2
    • 3
  1. 1.Theoretical PhysicsUniversity of OxfordOxfordUK
  2. 2.International School for Advanced StudiesTriesteItaly
  3. 3.Istituto Nazionale di Fisica NucleareTriesteItaly

Personalised recommendations