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

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.

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References

  1. 1.

    T. D. Lee and C. N. Yang,Phys. Rev. 87:404–409, 410–419 (1952).

  2. 2.

    R. B. Potts,Proc. Camb. Phil. Soc. 48:106 (1952).

  3. 3.

    F. Y. Wu,Rev. Mod. Phys. 54:235 (1982).

  4. 4.

    R. J. Baxter,J. Phys. A 20:5241–5261 (1987).

  5. 5.

    P. P. Martin and J. M. Maillard,J. Phys. A 19:L547-L551 (1986).

  6. 6.

    P. P. Martin,Nucl. Phys. B 225:497–504 (1983).

  7. 7.

    P. Martin,Potts Models and Related Problems in Statistical Mechanics (World Scientific, Singapore, 1991).

  8. 8.

    R. J. Baxter,J. Stat. Phys. 28:1–41 (1982).

  9. 9.

    R. J. BaxterJ. Phys. C 6:L445-L448 (1973).

  10. 10.

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

  11. 11.

    R. Kedem and B. M. McCoy,J. Stat. Phys. 71:865–901 (1993).

  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).

  13. 13.

    R. J. Baxter, J. H. H. Perk, and H. Au-Yang,Phys. Lett. A 128:138–142 (1988).

  14. 14.

    R. J. Baxter, V. V. Bazhanov, and J. H. H. Perk,Int. J. Mod. Phys. B 4:803–870 (1990)

  15. 15.

    V. A. Fateev and A. B. Zamolodchikov,Phys. Lett. A 92:37–39 (1982).

  16. 16.

    M. Kashiwara and T. Miwa,Nucl. Phys. B 275:121–134 (1986).

  17. 17.

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

  18. 18.

    D. E. Knuth,The Art of Computer Programming, Vol. 2-Semi-Numerical Algorithms (Addison-Wesley, Reading, Massachusetts, 1969).

  19. 19.

    B. M. McCoy and T. T. Wu,The Two-Dimensional Ising Model (Harvard University Press, Cambridge, Massachusetts, 1973).

  20. 20.

    P. A. Pearce,Int. J. Mod. Phys. B 4:715–734 (1990).

  21. 21.

    P. Christe and M. Henkel,Introduction to Conformal Invariance and Its Applications to Critical Phenomena (Springer-Verlag, Berlin, 1993).

  22. 22.

    J. L. Cardy, inPhase Transitions and Critical Phenomena, Vol. 11, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1987).

  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).

  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).

  25. 25.

    A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov,Nucl. Phys. B 241:333–380 (1984).

  26. 26.

    A. Cappelli, C. Itzykson, and J.-B. Zuber,Nucl. Phys. B 280:445–465 (1987).

  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).

  28. 28.

    VI. S. Dotsenko,Nucl. Phys. B 235:54–74 (1984).

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O'Rourke, M.J., Baxter, R.J. & Bazhanov, V.V. Numerical results for the three-state critical Potts model on finite rectangular lattices. J Stat Phys 78, 665–680 (1995). https://doi.org/10.1007/BF02183683

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Key Words

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