Skip to main content
Log in

Rigid interfaces for lattice models at low temperatures

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

Lattice models (on a hypercubic lattice of dimension larger than or equal to three) with spins attaining a finite number of values and finite-range interactions at low temperatures are considered. The existence of rigid interfaces as well as of surface tension under appropriate conditions is proven and the properties of corresponding Gibbs states are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. S. A. Pirogov and Ya. G. Sinai,Teor. Mat. Fiz. 25:358–369 (1975);26:61–76 (1976) [Theor. Math. Phys. 25:1185 (1975);26:39 (1976)].

    Google Scholar 

  2. Ya. G. Sinai,Theory of Phase Transitions: Rigorous Results (Akademiai Kiado, Budapest, 1982).

    Google Scholar 

  3. R. L. Dobrushin,Teor. Veroyat. Primen. 17:619–639 (1972) [Theory Prob. Appl. 17:582 (1972)].

    Google Scholar 

  4. J. Bricmont, J. L. Lebowitz, C. E. Pfister, and E. Olivieri,Commun. Math. Phys. 66:1–20 (1979)

    Google Scholar 

  5. J. Bricmont, J. L. Lebowitz, and C. E. Pfister,Commun. Math. Phys. 66:21–36;69:267–291 (1979).

    Google Scholar 

  6. C. Borgs,Commun. Math. Phys. 96:251–284 (1984).

    Google Scholar 

  7. J. Bricmont, K. Kuroda, and J. L. Lebowitz,J. Stat. Phys. 33:59–75 (1983).

    Google Scholar 

  8. J. Bricmont and J. Fröhlich,Commun. Math. Phys. 98:553–578 (1985).

    Google Scholar 

  9. M. Zahradník, inProceedings of Les Hauches 1984 Summer School. Critical Phenomena, Random Systems and Gauge Theories, K. Osterwalder and R. Stora, eds. (North-Holland, to appear).

  10. R. Kotecký and D. Preiss,Commun. Math. Phys. 103:491–498 (1986).

    Google Scholar 

  11. R. L. Dobrushin,Teor. Veroyat. Primen. 13:201–229 (1968) [Theory Prob. Appl. 13:197 (1968)]; J. Bricmont, J. L. Lebowitz, and C. E. Pfister,J. Stat. Phys. 21:573–581 (1979).

    Google Scholar 

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

    Google Scholar 

  13. R. L. Dobrushin,Teor. Veroyat. Primen. 18:261–279 (1973) [Theory Prob. Appl. 18:253 (1973)].

    Google Scholar 

  14. R. Kotecký and D. Preiss,Rend. Circ. Mat. Palermo, Ser. II 3:161–164 (1984).

    Google Scholar 

  15. D. Preiss, unpublished; M. Zahradník,Commun. Math. Phys. 93:559–581 (1984).

  16. R. Kotecký and D. Preiss, unpublished.

  17. J. Navrátil, Contour models and unicity of random fields, Thesis, Charles University, Prague (1982) [in Czech].

    Google Scholar 

  18. K. Kuratowski,Topology, Vol. 2 (Academic Press, New York, 1968).

    Google Scholar 

  19. C. Gruber and H. Kunz,Commun. Math. Phys. 22:133–161 (1971).

    Google Scholar 

  20. G. Gallavotti, A. Martin-Löf, and S. Miracle-Solé, inBattelle Seattle 1971 Rencontres, A. Lenard, ed. (Lecture Notes in Physics, Vol. 20, Springer, Berlin, 1973), pp. 162–204.

    Google Scholar 

  21. O. Ore,Theory of Graphs (AMS Colloquium Publication, Vol. 38, Providence, Rhode Island, 1962).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Holický, P., Kotecký, R. & Zahradník, M. Rigid interfaces for lattice models at low temperatures. J Stat Phys 50, 755–812 (1988). https://doi.org/10.1007/BF01026500

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01026500

Key words

Navigation