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Roughening transition for the Ising model on a BCC lattice. A case in the theory of ground states

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Abstract

For the Ising model on a bcc lattice we analyze the ground states associated with different interfaces and discuss some consequences on the roughening transition.

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References

  1. C. Rottman and M. Wortis,Phys. Rep. 103:59 (1984).

    Google Scholar 

  2. H. van Beijeren and I. Nolden, The roughening transition, to be published.

  3. D. B. Abraham, Surface structures and phase transitions-Exact results, in Phase Transitions and Critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, London).

  4. S. Balibar and B. Castaing, Helium: Solid-liquid interfaces,Surf. Sci. Rep. 5:87 (1985).

    Google Scholar 

  5. H. van Beijeren,Phys. Rev. Lett. 38:993 (1977).

    Google Scholar 

  6. H. W. J. Blöte and H. J. Hilhorst,J. Phys. A 15:L631 (1982).

    Google Scholar 

  7. B. Nienhuis, H. J. Hilhorst, and H. W. J. Blöte,J. Phys. A 17:3559 (1984).

    Google Scholar 

  8. R. L. Dobrushin, R. Kotecký, and S. B. Shlosman, in preparation.

  9. R. L. Dobrushin and S. B. Shlosman,Sov. Sci. Rev. C 5:54 (1985).

    Google Scholar 

  10. R. Kotecký and S. Miracle-Sole,Phys. Rev. B 34:2049 (1986).

    Google Scholar 

  11. R. Kotecký and S. Miracle-Sole, inVIIIth International Congress on Mathematical Physics, R. Séneor and M. Mebkhout, eds. (World Scientific, Singapore).

  12. Ya. G. Sinai,Theory of Phase Transitions: Rigorous Results (Pergamon, New York, 1982).

    Google Scholar 

  13. R. Kotecký,Phys. Rev. B 31:3088 (1985).

    Google Scholar 

  14. S. Pirogov and Ya. G. Sinaï,Teor. Mat. Fiz. 25:1185 (1975);26:39 (1976).

    Google Scholar 

  15. P. Holický, R. Kotecký, and M. Zahradník, Rigid interfaces for lattice models at low temperatures, Preprint, Marseille (1986).

  16. J. R. Banavar, D. Jasnow, and D. P. Landau,Phys. Rev. B 20:3820 (1979).

    Google Scholar 

  17. R. L. Dobrushin,Theory Prob. Appl. 17:582 (1972).

    Google Scholar 

  18. H. van Beijeren,Commun. Math. Phys. 40:1 (1975).

    Google Scholar 

  19. J. Fröhlich, C. E. Pfister, and T. Spencer, inStochastic Processes in Quantum Theory and Statistical Physics, S. Albeverio, Ph. Combe, and M. Sirugue-Collin, eds. (Lecture Notes in Physics, Vol. 173, Springer, Berlin, 1982), p. 169.

    Google Scholar 

  20. J. Bricmont, J. R. Fontaine, and J. L. Lebowitz,J. Stat. Phys. 29:193 (1982).

    Google Scholar 

  21. J. L. Lebowitz,Commun. Math. Phys. 35:87 (1974).

    Google Scholar 

  22. J. Bricmont, A. El Mellouki, and J. Fröhlich,J. Stat. Phys. 42:743 (1986).

    Google Scholar 

  23. G. Gallavotti,Commun. Math. Phys. 27:103 (1972).

    Google Scholar 

  24. C. Jayaprakash, W. F. Saam, and S. Teitel,Phys. Rev. Lett. 50:2017 (1983).

    Google Scholar 

  25. C. Jayaprakash and W. F. Saam,Phys. Rev. B 30:3916 (1984).

    Google Scholar 

  26. J. Bricmont, J. L. Lebowitz, C. E. Pfister, and E. Olivieri,Commun. Math. Phys. 66:1 (1979); J. Bricmont, J. L. Lebowitz, and C. E. Pfister,Commun. Math. Phys. 66:21 (1979);69:267 (1979).

    Google Scholar 

  27. E. H. Lieb and F. Y. Wu, inPhase Transitions and Critical Phenomena, Vol. 1, C. Domb and M. S. Green, eds. (Academic Press, London, 1972).

    Google Scholar 

  28. J. B. Sutherland, C. N. Yang, and C. P. Yang,Phys. Rev. Lett. 19:588 (1967).

    Google Scholar 

  29. A. F. Andreev,Zh. Eksp. Teor. Fiz. 80:2042 (1981) [Sov. Phys. JETP 53:1063 (1982)].

    Google Scholar 

  30. J. Miekisz, Classical lattice gas model with a unique nondegenerate but unstable periodic ground state configuration, Preprint.

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Kotecký, R., Miracle-Sole, S. Roughening transition for the Ising model on a BCC lattice. A case in the theory of ground states. J Stat Phys 47, 773–799 (1987). https://doi.org/10.1007/BF01206158

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  • DOI: https://doi.org/10.1007/BF01206158

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