Journal of Statistical Physics

, Volume 78, Issue 3–4, pp 665–680 | Cite as

Numerical results for the three-state critical Potts model on finite rectangular lattices

  • M. J. O'Rourke
  • R. J. Baxter
  • V. V. Bazhanov
Articles

Abstract

Partition functions for the three-state critical Potts model on finite square lattices and for a variety of boundary conditions are presented. The distribution of their zeros in the complex plane of the spectral variable is examined and is compared to the expected infinite-lattice result. The partition functions are then used to test the finite-size scaling predictions of conformal and modular invariance.

Key Words

Statistical mechanics lattice statistics solvable models three-state Potts model zeros of the partition function conformal invariance modular invariance 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    T. D. Lee and C. N. Yang,Phys. Rev. 87:404–409, 410–419 (1952).Google Scholar
  2. 2.
    R. B. Potts,Proc. Camb. Phil. Soc. 48:106 (1952).Google Scholar
  3. 3.
    F. Y. Wu,Rev. Mod. Phys. 54:235 (1982).Google Scholar
  4. 4.
    R. J. Baxter,J. Phys. A 20:5241–5261 (1987).Google Scholar
  5. 5.
    P. P. Martin and J. M. Maillard,J. Phys. A 19:L547-L551 (1986).Google Scholar
  6. 6.
    P. P. Martin,Nucl. Phys. B 225:497–504 (1983).Google Scholar
  7. 7.
    P. Martin,Potts Models and Related Problems in Statistical Mechanics (World Scientific, Singapore, 1991).Google Scholar
  8. 8.
    R. J. Baxter,J. Stat. Phys. 28:1–41 (1982).Google Scholar
  9. 9.
    R. J. BaxterJ. Phys. C 6:L445-L448 (1973).Google Scholar
  10. 10.
    G. Albertini, S. Dasmahapatra, and B. M. McCoy,Int. J. Mod. Phys. A 7 (Suppl. 1A):1 (1992).Google Scholar
  11. 11.
    R. Kedem and B. M. McCoy,J. Stat. Phys. 71:865–901 (1993).Google Scholar
  12. 12.
    J. L. Cardy, Conformal invariance and statistical mechanics, inLes Houches, Session XLIV, Fields, Strings and Critical Phenomena, E. Brézin and J. Zinn-Justin, eds. (1989).Google Scholar
  13. 13.
    R. J. Baxter, J. H. H. Perk, and H. Au-Yang,Phys. Lett. A 128:138–142 (1988).Google Scholar
  14. 14.
    R. J. Baxter, V. V. Bazhanov, and J. H. H. Perk,Int. J. Mod. Phys. B 4:803–870 (1990)Google Scholar
  15. 15.
    V. A. Fateev and A. B. Zamolodchikov,Phys. Lett. A 92:37–39 (1982).Google Scholar
  16. 16.
    M. Kashiwara and T. Miwa,Nucl. Phys. B 275:121–134 (1986).Google Scholar
  17. 17.
    R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).Google Scholar
  18. 18.
    D. E. Knuth,The Art of Computer Programming, Vol. 2-Semi-Numerical Algorithms (Addison-Wesley, Reading, Massachusetts, 1969).Google Scholar
  19. 19.
    B. M. McCoy and T. T. Wu,The Two-Dimensional Ising Model (Harvard University Press, Cambridge, Massachusetts, 1973).Google Scholar
  20. 20.
    P. A. Pearce,Int. J. Mod. Phys. B 4:715–734 (1990).Google Scholar
  21. 21.
    P. Christe and M. Henkel,Introduction to Conformal Invariance and Its Applications to Critical Phenomena (Springer-Verlag, Berlin, 1993).Google Scholar
  22. 22.
    J. L. Cardy, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987).Google Scholar
  23. 23.
    C. Itzykson, inProceedings First Asia Pacific Workshop on High Energy Physics, B. E. Baaquie, C. K. Chew, C. H. Oh, and K. K. Phua, eds. (World Scientific, Singapore, 1987).Google Scholar
  24. 24.
    L. P. Kadanoff, W. Goetze, D. Hamblen, R. Hecht, E. A. S. Lewis, V. V. Palciauskas, M. Rayl, and J. Swift,Rev. Mod. Phys. 39:395–431 (1967).Google Scholar
  25. 25.
    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,Nucl. Phys. B 241:333–380 (1984).Google Scholar
  26. 26.
    A. Cappelli, C. Itzykson, and J.-B. Zuber,Nucl. Phys. B 280:445–465 (1987).Google Scholar
  27. 27.
    D. Friedan, Z. Qiu, and S. Shenker,Phys. Rev. Lett. 52:1575–1578 (1984); inVertex Operators in Mathematics and Physics, J. Lepowsky, S. Mandelstam, and I. Singer, eds. (Springer, New York, 1985).Google Scholar
  28. 28.
    VI. S. Dotsenko,Nucl. Phys. B 235:54–74 (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • M. J. O'Rourke
    • 1
  • R. J. Baxter
    • 2
  • V. V. Bazhanov
    • 2
  1. 1.Theoretical Physics, I.A.S.Australian National UniversityCanberraAustralia
  2. 2.Theoretical Physics, I.A.S., and School of Mathematical SciencesAustralian National UniversityCanberraAustralia

Personalised recommendations