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First-order phase transitions in large entropy lattice models

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Abstract

We show the existence of a first-order phase transition in thev-dimensional Potts model forv≧2, when the number of states of a single spin is big enough. Low-temperature pure phases are proved to survive up to the critical temperature. Also the existence of a first-order transition in thev-dimensional Potts gauge model,v≧3, is obtained if the underlying gauge group is finite but large.

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References

  1. Potts, R.B.: Proc. Camb. Philos. Soc.48, 106–109 (1952)

    Google Scholar 

  2. Wu, F.Y.: The Potts Model (to be published)

  3. Hintermann, A., Kunz, H., Wu, F.Y.: J. Stat. Phys.19, 623–632 (1978)

    Google Scholar 

  4. Baxter, R.J., Temperley, H.N.V., Ashley, S.E.: Proc. R. Soc. Lond. A358, 535–559 (1978)

    Google Scholar 

  5. Pearce, P.A., Griffiths, R.B.: J. Phys. A.: Math. Gen.13, 2143–2148 (1980)

    Google Scholar 

  6. Kogut, J.B.: Phys. Rev. D21, 2316–2326 (1980)

    Google Scholar 

  7. Wegner, F.J.: J. Math. Phys.12, 2259–2272 (1971)

    Google Scholar 

  8. Balian, R., Drouffe, J.M., Itzykson, C.: Phys. Rev. D11, 2098–2103 (1975)

    Google Scholar 

  9. Creutz, M., Jacobs, L., Rebbi, C.: Phys. Rev. Lett.42, 1390–1393 (1979)

    Google Scholar 

  10. Ginsparg, P., Goldschmidt, Y.Y., Zuber, J.-B.: Nucl. Phys. B170 FS 1, 409–432 (1980)

    Google Scholar 

  11. Kotecký, R.: Commun. Math. Phys.82, 391–397 (1981)

    Google Scholar 

  12. Dobrushin, R.L., Shlosman, S.B.: Phases corresponding to the local energy minima (in print)

  13. Glimm, J., Jaffe, A., Spencer, T.: Commun. Math. Phys.45, 203–216 (1975)

    Google Scholar 

  14. Fröhlich, J., Lieb, E.: Commun. Math. Phys.60, 233–267 (1978)

    Google Scholar 

  15. Fröhlich, J., Israel, R., Lieb, E., Simon, B.: Commun. Math. Phys.62, 1–37 (1978)

    Google Scholar 

  16. Fröhlich, J., Israel, R., Lieb, E., Simon, B.: J. Stat. Phys.22, 297–347 (1980)

    Google Scholar 

  17. Preston, C.: Random fields. In: Lecture Note in Mathematics, Vol. 534. Dold, A., Eckmann, B. (eds.) Berlin, Heidelberg, New York: Springer 1976

    Google Scholar 

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Author notes

  1. R. Kotecký

    Present address: Department of Mathematical Physics, Charles University, Povltavská 1, 18000, Praha 8, Pelc-Tyrolka, Czechoslovakia

Authors and Affiliations

  1. I.H.E.S., F-91440, Bures-sur-Yvette, France

    R. Kotecký

  2. Institute for Problems of Information Transmission, Academy of Sciences, Moscow, USSR

    S. B. Shlosman

Authors
  1. R. Kotecký
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  2. S. B. Shlosman
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Communicated by E. Lieb

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Kotecký, R., Shlosman, S.B. First-order phase transitions in large entropy lattice models. Commun.Math. Phys. 83, 493–515 (1982). https://doi.org/10.1007/BF01208713

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  • DOI: https://doi.org/10.1007/BF01208713

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