Skip to main content
SpringerLink
Log in

Virasoro characters from bethe equations for the critical ferromagnetic three-state potts model

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We obtain new fermionic sum representations for the Virasoro characters of the conformal field theory describing the ferromagnetic three-state Potts spin chain. These arise from the fermionic quasiparticle excitations derived from the Bethe equations for the eigenvalues of the Hamiltonian. In the conformal scaling limit, the Bethe equations provide a description of the spectrum in terms of one genuine quasiparticle and two “ghost” excitations with a limited microscopic momentum range. This description is reflected in the structure of the character formulas, and suggests a connection with the integrable perturbation of dimensions (2/3, 2/3)+ which breaks theS 3 symmetry of the conformal field theory down toZ 2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. H. N. V. Temperley and E. H. Lieb,Proc. R. Soc. Lond. A. 322:251 (1971).

    Google Scholar 

  2. R. J. Baxter,J. Phys. C 6:L445 (1973).

    Google Scholar 

  3. R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

    Google Scholar 

  4. R. Kedem and B. M. McCoy,J. Stat. Phys. 71:883 (1993).

    Google Scholar 

  5. G. Albertini, S. Dasmahapatra, and B. M. McCoy,Phys. Lett. A 170:397 (1992).

    Google Scholar 

  6. R. J. Baxter and P. A. Pearce,J. Phys. A 15:897 (1982).

    Google Scholar 

  7. V. V. Bazhanov and N. Yu. Reshetikhin,Int. J. Mod. Phys. A 4:115 (1989).

    Google Scholar 

  8. G. Albertini, B. M. McCoy, and J. H. H. Perk,Phys. Lett. A. 135:159 (1989); and inAdvanced Studies in Pure Mathematics, 19th ed., M. Jimbo, T. Miwa, and A. Tsuchiya, eds. (Kinokuniya-Academic, Tokyo, 1989), p. 1.

    Google Scholar 

  9. V. V. Bazhanov and Yu. G. Stroganov,J. Stat. Phys. 59:799 (1990).

    Google Scholar 

  10. R. J. Baxter, V. V. Bazhanov, and J. H. H. Perk,Int. J. Mod. Phys. B 4:803 (1990).

    Google Scholar 

  11. G. Albertini,J. Phys. A 25:1799 (1992).

    Google Scholar 

  12. P. A. Pearce,Int. J. Mod. Phys. A 7 (Suppl.1B):791 (1992).

    Google Scholar 

  13. J. Lepowsky and M. Prime,Structure of the Standard Modules for the Affine Lie Algebra A (1)1 (AMS, Providence, Rhode Island, 1985).

    Google Scholar 

  14. A. Rocha-Caridi, inVertex Operators in Mathematics and Physics, J. Lepowsky, S. Mandelstam, and I. M. Singer, eds. (Springer, Berlin, 1985), p. 451.

    Google Scholar 

  15. V. S. Dotsenko,Nucl. Phys. B 235 [FS11]:54 (1984).

    Google Scholar 

  16. A. B. Zamolodchikov and V. A. Fateev,Sov. Phys. JETP 62:215 (1985).

    Google Scholar 

  17. J. L. Cardy,Nucl. Phys. B 275[FS17]:200 (1986).

    Google Scholar 

  18. R. Kedem, T. R. Klassen, B. M. McCoy, and E. Melzer,Phys. Lett. B 307:68 (1993).

    Google Scholar 

  19. R. Kedem,J. Stat. Phys. 71:903 (1993).

    Google Scholar 

  20. D. Gepner and Z. Qiu,Nucl. Phys. B 285[FS19]:423 (1987).

    Google Scholar 

  21. G. Albertini, S. Dasmahapatra, and B. M. McCoy,Int. J. Mod. Phys. A 7(Suppl. 1A):1 (1992).

    Google Scholar 

  22. A. Klümper and P. A. Pearce,J. Stat. Phys. 64:13 (1991);Physica A 183:304 (1992).

    Google Scholar 

  23. R. P. Stanley,Ordered Structures and Partitions (AMS, Providence, Rhode Island, 1972).

    Google Scholar 

  24. G. E. Andrews,The Theory of Partitions (Addison-Wesley, London, 1976).

    Google Scholar 

  25. V. G. Kac and D. H. Peterson,Adv. Math. 53:125 (1984).

    Google Scholar 

  26. M. Jimbo and T. Miwa,Adv. Stud. Pure Math. 4:97 (1984).

    Google Scholar 

  27. P. Goddard, A. Kent, and D. Olive,Commun. Math. Phys. 103:105 (1986).

    Google Scholar 

  28. B. L. Feigin and D. B. Fuchs,Funct. Anal. Appl. 17:241 (1983).

    Google Scholar 

  29. G. Felder,Nucl. Phys. B 317:215 (1989).

    Google Scholar 

  30. A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,J. Stat. Phys. 34:763 (1984);Nucl. Phys. B 241:337 (1984).

    Google Scholar 

  31. V. A. Fateev and A. B. Zamolodchikov,Nucl. Phys. B 280 [FS18]:644 (1987).

    Google Scholar 

  32. D. Altschuler, M. Bauer, and H. Saleur,J. Phys. A 23:L789 (1990).

    Google Scholar 

  33. J. Distler and Z. Qiu,Nucl. Phys. B 336:533 (1990).

    Google Scholar 

  34. R. Kedem, T. R. Klassen, B. M. McCoy, and E. Melzer,Phys. Lett. B 304:263 (1993).

    Google Scholar 

  35. A. B. Zamolodchikov, inAdvanced Studies in Pure Mathematics, 19th ed., M. Jimbo, T. Miwa, and A. Tsuchiya, eds. (Kinokuniya-Academic, Tokyo, 1989), p. 641.

    Google Scholar 

  36. A. B. Zamolodchikov,Int. J. Mod. Phys. A 3:743 (1988).

    Google Scholar 

  37. R. Köberle and J. A. Swieca,Phys. Lett. B,86:209 (1979).

    Google Scholar 

  38. R. J. Baxter,J. Phys. A 13:L61 (1980);J. Stat. Phys. 26:427 (1981).

    Google Scholar 

  39. M. Kashiwara and T. Miwa,Nucl. Phys. B 275:121 (1986).

    Google Scholar 

  40. V. Pasquier,J. Phys. A 20:L217 and L221 (1987).

    Google Scholar 

  41. G. E. Andrews, R. J. Baxter, and P. J. Forrester,J. Stat. Phys. 35:193 (1984).

    Google Scholar 

  42. P. Fendley and P. Ginsparg,Nucl. Phys. B 324:549 (1989).

    Google Scholar 

  43. A. B. Zamolodchikov,Sov. J. Nucl. Phys. 46:1090 (1987).

    Google Scholar 

  44. A. Ludwig and J. L. Cardy,Nucl. Phys. B 285[FS19]:687 (1987).

    Google Scholar 

  45. A. B. Zamolodchikov, Landau Institute preprint (1989).

  46. D. Bernard and A. LeClair,Nucl. Phys. B 340:721 (1990).

    Google Scholar 

  47. N. Yu. Reshetikhin and F. A. Smirnov,Common. Math. Phys. 131:157 (1990).

    Google Scholar 

  48. A. B. Zamolodchikov,Nucl. Phys. B. 358:497, 524 (1991).

    Google Scholar 

  49. V. A. Fateev and A. B. Zamolodchikov,Phys. Lett. B 271:91 (1991).

    Google Scholar 

  50. T. R. Klassen and E. Melzer,Nucl. Phys. B 370:511 (1992).

    Google Scholar 

  51. F. Ravanini,Phys. Lett. B 274:345 (1992).

    Google Scholar 

  52. T. R. Klassen and E. Melzer,Nucl. Phys. B, in press; preprint hep-th/9110047.

  53. V. V. Bazhanov and N. Yu. Reshetikhin,Progr. Theor. Phys. Suppl. 102:301 (1990).

    Google Scholar 

  54. J. L. Cardy, inFields, Strings, and Critical Phenomena, Les Houches 1988, E. Brézin and J. Zinn-Justin, eds., (North-Holland, Amsterdam, 1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. High Energy Physics, ICTP, I-34100, Trieste, Italy

    Srinandan Dasmahapatra

  2. Institute for Theoretical Physics, SUNY, 11794-3840, Stony Brook, New York

    Rinat Kedem, Barry M. McCoy & Ezer Melzer

Authors
  1. Srinandan Dasmahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rinat Kedem
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Barry M. McCoy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ezer Melzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dasmahapatra, S., Kedem, R., McCoy, B.M. et al. Virasoro characters from bethe equations for the critical ferromagnetic three-state potts model. J Stat Phys 74, 239–274 (1994). https://doi.org/10.1007/BF02186814

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02186814

Key Words

Search

Navigation