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Conformal Invariance — a Survey of Principles with Applications to Statistical Mechanics and Surface Physics

  • Peter Kleban
Part of the NATO ASI Series book series (NSSB, volume 218)

Abstract

These lectures are a brief survey of the basic principles of conformal invariance with examples and applications to statistical mechanical models, mainly in two-dimensions, and real surface systems. Given the amount of time available, we cannot even hope to be complete—note that the introductory lectures by Ginsparg [1] took up more than 13 hours! We will attempt only to outline the basic theory and present some consequences and examples of interest to the author. Hopefully this will suffice to convey a feeling for the subject, some appreciation of its implications, and more importantly stimulate the reader to further study. To this end, more exhaustive treatments may be found in various review articles [1–6]. A few comments on the approach and level of these papers are given below.

Keywords

Half Plane Multiple Scattering Conformal Transformation Conformal Invariance Operator Product Expansion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Ginsparg, in Champs, Cordes, et Phénomènes Critiques/Fields, Strings, and Critical Phenomena, edited by E. Brézin and J. Zinn-Justin, Elsevier Publishers B.V. (to appear).Google Scholar
  2. 2.
    J. L. Cardy, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. L. Lebowitz (Academic, London, 1986) Vol. 11.Google Scholar
  3. 3.
    J. L. Cardy, in Champs, Cordes, et Phénomènes Critiques/Fields, Strings, and Critical Phenomena, edited by E. Brézin and J. Zinn-Justin, Elsevier Publishers B.V. (to appear).Google Scholar
  4. 4.
    I. Affleck, in Champs, Cordes, et Phénomènes Critiques/Fields, Strings, and Critical Phenomena, edited by E. Brézin and J. Zinn-Justin, Elsevier Publishers B.V. (to appear).Google Scholar
  5. 5.
    A. A. Belavin, A. M. Polyakov and A. B. Zamolodchikov, Nucl. Phys. B 241, 333 (1984).MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    Conformai Invariance and Applications to Statistical Mechanics, editors C. Itzykson et al., World Scientific Publishing (1988).Google Scholar
  7. 7.
    A. M. Polyakov, Sov. Phys. JETP Letters 12, 381 (1970).ADSGoogle Scholar
  8. 8.
    L. Schaefer, J. Phys. A 9, 377 (1976).MathSciNetADSCrossRefGoogle Scholar
  9. 9.
    L. P. Kadanoff, Phys. Rev. Letters 23, 1430 (1969); A. M. Polyakov, Sov. Phys. JETP 30, 151 (1969); K. G. Wilson, Phys. Rev. 179, 1499 (1969).ADSCrossRefGoogle Scholar
  10. 10.
    J. L Cardy, J. Phys. A 17, L385 (1984).MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    R. Hentschke, P. Kleban and G. Akinci, J. Phys. A 19, 3353 (1986).ADSCrossRefGoogle Scholar
  12. 12.
    M. Abramowitz and I. A. Stegun, editors, Handbook of Mathematical Functions, (Dover, 1972).Google Scholar
  13. 13.
    M. E. Fisher and P. G. deGennes, C. R. Acad. Sci. Paris 287, B-207 (1978).Google Scholar
  14. 14.
    T. W. Burkhardt and E. Eisenriegler, J. Phys. A 18, L83 (1985).MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    H. W. J. Blöte, J. L. Cardy, and M. P. Nightingale, Phys. Rev. Letters 56, 742 (1986); I. Affleck, Phys. Rev. Letters 56, 746 (1986).ADSCrossRefGoogle Scholar
  16. 16.
    D. Friedan, Z. Qiu and S. Shenker, Phys. Rev. Letters 52, 1575 (1984).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    J. L. Cardy, Nucl. Phys. B 240 [FS12], 514 (1984).ADSCrossRefGoogle Scholar
  18. 18.
    I. Robinson, Phys. Rev. Letters 50, 1145 (1983) and references therein; I. Robinson, Y. Kuk and L.C. Feldman, Phys. Rev. B 29, 4762 (1984) and references therein.ADSCrossRefGoogle Scholar
  19. 19.
    J. C. Campuzano, M. S. Foster, G. Jennings, R. F. Willis and W. N. Unertl, Phys. Rev. Letters 54, 2684 (1985); J. C. Campuzano, G. Jennings and R. F. Willis, Surface Sci. 162, 484 (1985).ADSCrossRefGoogle Scholar
  20. 20.
    W. N. Unertl, private communication.Google Scholar
  21. 21.
    P. Kleban, G. Akinci, R. Hentschke and K. R. Brownstein, J. Phys. A 19, 437 (1986); Surface Sci. 166, 159 (1986).ADSCrossRefGoogle Scholar
  22. 22.
    P. Kleban and R. Hentschke, Phys. Rev. B 34, 1980 (1986).ADSCrossRefGoogle Scholar
  23. 23.
    D. E. Clark, W. N. Unertl and P. Kleban, Phys. Rev. B 34, 4379 (1986).ADSCrossRefGoogle Scholar
  24. 24.
    P. Bak, Solid State Commun. 32, 581 (1979).ADSCrossRefGoogle Scholar
  25. 25.
    P. Kleban, R. Hentschke and J. C. Campuzano, Phys. Rev. B 37, 5738 (1988).ADSCrossRefGoogle Scholar
  26. 26.
    P. Piercy and H. Pfnür, Phys. Rev. Lett. 59, 1124 (1987).ADSCrossRefGoogle Scholar
  27. 27.
    See, for example, B. Salanon et al, J. Vac. Sci. Technol. A 6, 655 (1988) or G. A. Held et al, Phys. Rev. Lett. 59, 2075 (1987) and references therein.ADSCrossRefGoogle Scholar
  28. 28.
    S.G.J. Mochrie, Phys. Rev. Letters 59, 3047 (1987); P. Zeppenfeld, K. Kern, R. David and G. Comsa, Phys. Rev. Letters 62, 63 (1989); S. Thevusathan, thesis, Univ. of Maine (1989).CrossRefGoogle Scholar
  29. 29.
    See W. N. Unertl, Comments Cond. Mat. Phys. 12, 289 (1986); M. Schick, Prog. Surface Sci. 11, 245 (1981).Google Scholar
  30. 30.
    A. B. Zamolodchikov and V. A. Fateev, Sov. Phys. JETP 62, 215 (1985).MathSciNetGoogle Scholar
  31. 31.
    C. B. Duke and A. Liebsch, Phys. Rev. B 9, 1126 (1974).ADSCrossRefGoogle Scholar
  32. 32.
    R. Hentschke and P. Kleban, Surface Sci. 202, 533 (1988).ADSCrossRefGoogle Scholar
  33. 33.
    P. Di Francesco, H. Saleur and J. B. Zuber, Nuclear Phys. B 290 [FS20], 527 (1987).MathSciNetADSCrossRefGoogle Scholar
  34. 34.
    S. Y. Tong, private communication.Google Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Peter Kleban
    • 1
  1. 1.Materials Science DivisionArgonne National LaboratoryUSA

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