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Inversion relations, phase transitions and transfer matrix excitations for special spin models in two dimensions

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Zeitschrift für Physik B Condensed Matter

Abstract

For a special class of “Interaction-Round-Faces’ models (SIRF) which include the eightvertex model and the standard Potts model in a decoupling limit we derive inversion relations both for the partition function and the transfer matrix. These relations lead to some new exact results. In the general case the location of phase transitions is determined which reduces to known results for the Potts model. For the (solvable) self-dual Potts model we calculate all eigenvalues of the transfer matrix, i.e. the excitations of the model, from which the exact correlation length is derived.

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References

  1. Baxter, R.J.: Exactly solved models in statistical mechanics. London: Academic Press 1982

    Google Scholar 

  2. Stroganov, Y.G.: Phys. Lett.74A, 116 (1979)

    Google Scholar 

  3. Klümper, A., Zittartz, J.: Z. Phys. B — Condensed Matter71, 495 (1988)

    Google Scholar 

  4. Klümper, A.: Diplom-Arbeit, Universität zu Köln 1987 (unpublished)

  5. Klümper, A., Zittartz, J.: Z. Phys. B — Condensed Matter75, 371 (1989)

    Google Scholar 

  6. Baxter, R.J.: J. Phys. C6, L445 (1973)

    Google Scholar 

  7. Baxter, R.J.: Proc. R. Soc. London Ser. A383, 43 (1982)

    Google Scholar 

  8. Maillard, J.M., Rammal, R.: J. Phys. A16, 353 (1983)

    Google Scholar 

  9. Jaekel, M.T., Maillard, J.M.: J. Phys. A15, 2241 (1982)

    Google Scholar 

  10. Pearce, P.A.: Phys. Rev. Lett.58, 1502 (1987)

    Google Scholar 

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

    Google Scholar 

  12. Kramers, H.A., Wannier, G.H.: Phys. Rev.60, 252 (1941)

    Google Scholar 

  13. Hintermann, A., Kunz, H., Wu, F.Y.: J. Stat. Phys.19, 623 (1978)

    Google Scholar 

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

    Google Scholar 

  15. Pearce, P.A.: J. Phys. A20, 6463 (1987)

    Google Scholar 

  16. Schadschneider, A.: Diplom-Arbeit, Universität zu Köln 1988 (unpublished)

  17. Johnson, J.D., Krinsky, S., McCoy, B.M.: Phys. Rev. A8, 2526 (1973)

    Google Scholar 

  18. Blöte, H.W., Nightingale, M.: Physica112A, 405 (1982)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-5000, Köln 41, Federal Republic of Germany

    A. Klümper, A. Schadschneider & J. Zittartz

Authors
  1. A. Klümper
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  2. A. Schadschneider
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  3. J. Zittartz
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Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich

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Klümper, A., Schadschneider, A. & Zittartz, J. Inversion relations, phase transitions and transfer matrix excitations for special spin models in two dimensions. Z. Physik B - Condensed Matter 76, 247–258 (1989). https://doi.org/10.1007/BF01312692

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  • DOI: https://doi.org/10.1007/BF01312692

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