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Analyticity and integrability in the chiral Potts model

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Abstract

We study the perturbation theory for the general nonintegrable chiral Potts model depending on two chiral angles and a strength parameter and show how the analyticity of the ground-state energy and correlation functions dramatically increases when the angles and the strength parameter satisfy the integrability condition. We further specialize to the superintegrable case and verify that a sum rule is obeyed.

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References

  1. R. J. Baxter, inFundamental Studies in Statistical Mechanics V, E. G. D. Cohen, ed. (North-Holland, Amsterdam, 1980), p. 109.

    Google Scholar 

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

  3. N. Seiberg,Phys. Lett. B 318:469 (1993);Phys. Rev. D 49:6857 (1994).

    Google Scholar 

  4. N. Seiberg and E. Witten,Nucl. Phys. B 426:12 (1994);431:482 (1994).

    Google Scholar 

  5. H. Au-Yang, B. M. McCoy, J. H. H. Perk, S. Tang, and M.-L. Yan,Phys. Lett. A 123:219 (1987).

    Google Scholar 

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

    Google Scholar 

  7. H. Au-Yang and J. H. H. Perk,Adv. Stud. Pure Math. 19:57 (1989).

    Google Scholar 

  8. G. Albertini, B. M. McCoy, and J. H. H. Perk,Adv. Stud. Pure Math. 19:1 (1989).

    Google Scholar 

  9. R. J. Baxter,Phys. Lett. A.146:110 (1990); Free energy of the chiral Potts model in the scaling region, Canberra preprint (1995).

    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, B. M. McCoy, J. H. H. Perk, and S. Tang,Nucl. Phys. B.314:159 (1989).

    Google Scholar 

  12. G. Albertini, B. M. McCoy, and J. H. H. Perk,Phys. Lett. A 135:159 (1989).

    Google Scholar 

  13. B. M. McCoy and W. P. Orrick,Nucl. Phys. B (Proc. Suppl.) A 45:50–61 (1996).

    Google Scholar 

  14. J. J. Sakurai,Modern Quantum Mechanics (Addison-Wesley, Reading, Massachusetts, 1985).

    Google Scholar 

  15. N. S. Han and A. Honecker,J. Phys. A 27:9 (1994).

    Google Scholar 

  16. A. Honecker, Quantum spin models and extended conformal algebra [Hepth 9503104].

  17. A. Honecker and G. von Gehlen,Nucl. Phys. B 435:505 (1985).

    Google Scholar 

  18. A. Honecker, A perturbative approach to the chiral Potts model [Hepth 9409122].

  19. I. G. Enting and A. J. Guttmann, The Ising model, self avoiding walks and solvability, Lattice '95 Proceedings,Nucl. Phys. B Suppl., submitted.

  20. T. T. Wu, B. M. McCoy, C. A. Tracy, and E. Barouch,Phys. Rev. B 13:316 (1976).

    Google Scholar 

  21. C. A. Tracy, inNonlinear Equations in Physics and Mathematics, A. O. Barut, ed. (Reidel, Dortrecht, Holland, 1978), p. 221.

    Google Scholar 

  22. R. J. Baxter,Phil. Trans. R. Soc. Lond. 289:315 (1978).

    Google Scholar 

  23. R. J. Baxter,J. Stat. Phys. 63:433 (1991);70:535 (1993).

    Google Scholar 

  24. S. Howes, L. P. Kadanoff, and M. den Nijs,Nucl. Phys. B 215 [FS7]:169 (1983).

    Google Scholar 

  25. A. Gervois and M. L. Mehta,J. Math. Phys. 36:5098 (1995).

    Google Scholar 

  26. S. Gasiorowicz,Quantum Physics (Wiley, New York, 1974).

    Google Scholar 

  27. A. Erdelyi,Higher Transcendental Functions, Vol. 1 (McGraw-Hill, New York, 1953).

    Google Scholar 

  28. L. Onsager,Phys. Rev. 65:117 (1944).

    Google Scholar 

  29. H. Rademacher and E. Grosswald,Dedekind Sums (Mathematical Association of America, 1972).

  30. M. Abramowitz and I. Stegun,Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (U. S. Government Printing Office, 1972).

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McCoy, B.M., Orrick, W.P. Analyticity and integrability in the chiral Potts model. J Stat Phys 83, 839–865 (1996). https://doi.org/10.1007/BF02179547

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