Skip to main content
Log in

Interface sharpness in the Potts model

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

Abstract

A simple proof is given for the existence of a sharp interface between two ordered phases for the three-dimensional 2n-state Potts model (n integer).

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.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. R. L. Dobrushin, Gibbs states describing the coexistence of phases for a three-dimensional Ising model,Theor. Prob. Appl. 17:582 (1972).

    Google Scholar 

  2. H. van Beijeren, Interface sharpness in the Ising system,Commun. Math. Phys. 40:1 (1975).

    Google Scholar 

  3. R. B. Potts, Some generalized order-disorder transformation,Proc. Camb. Philos. Soc. 48:106 (1952).

    Google Scholar 

  4. J. Bricmont, J. L. Lebowitz, and A. Messager, First order phase transition in Potts and Ising systems,Phys. Lett. A 95:169 (1983).

    Google Scholar 

  5. J. L. Lebowitz, G.H.S. and other inequalities,Commun. Math. Phys. 35:87 (1974).

    Google Scholar 

  6. C. M. Kasteleyn, P. W. Fortuin, and J. Ginibre, Correlation inequalities on some partially ordered sets,Commun. Math. Phys. 22:89 (1971).

    Google Scholar 

  7. J. De Coninck, A. Messager, S. Miracle-Sole, and J. Ruiz, A study of perfect wetting for Potts and Blume-Capel models with correlation inequalities,J. Stat. Phys. 52:45 (1988).

    Google Scholar 

  8. D. M. Martirosian, Translation invariant Gibbs states in theq-states Potts model,Commun. Math. Phys. 105:281 (1986).

    Google Scholar 

  9. R. B. Griffiths, Correlations in Ising ferromagnets II.J. Math. Phys. 8:484 (1967).

    Google Scholar 

  10. J. Ginibre, General formulation of Griffiths inequalities,Commun. Math. Phys. 16:310 (1970).

    Google Scholar 

  11. A. Messager, S. Miracle-Solé, and C.-E. Pfister, Correlation inequalities and uniqueness of the equilibrium state in the plane rotator ferromagnetic model,Commun. Math. Phys. 59:19 (1978).

    Google Scholar 

  12. C.-E. Pfister, Translation invariant equilibrium states of ferromagnetic Abelian lattice system,Commun. Math. Phys. 86:375 (1982).

    Google Scholar 

  13. L. Laanait, A. Messager, and J. Ruiz, Phases coexistence and surface tensions for the Potts model,Commun. Math. Phys. 105:572 (1986).

    Google Scholar 

  14. R. Kotecky, L. Laanait, A. Messager, and J. Ruiz, Theq-state Potts model in the standard Pirogov-Sinaï theory: Topological aspects, Preprint, CPT Marseille.

  15. R. Kotecky and S. B. Shlosman, First order phase transitions in large entropy lattice models,Commun. Math. Phys. 83:493 (1982).

    Google Scholar 

  16. A. Hintermann, H. Kunz, and F. Y. Wu, Exact results for the Potts model in two dimension,J. Stat. Phys. 19:623 (1978).

    Google Scholar 

  17. R. J. Baxter, Potts model at the critical temperature,J. Phys. C: Solid State Phys. 6:L445 (1973); Magnetization discontinuity of the two-dimensional Potts model,J. Phys. A: Math. Gen. 15:3329 (1982); see alsoExactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

    Google Scholar 

  18. J. K. Percus, Correlation inequalities for Ising spin lattices,Commun. Math. Phys. 40:283 (1975).

    Google Scholar 

  19. C. M. Fortuin and P. W. Kasteleyn, On the random cluster model,Physica 57:536 (1972).

    Google Scholar 

  20. F. Dunlop, L. Laanait, A. Messager, S. Miracle-Sole, and J. Ruiz, Preprint, CPT Marseille.

  21. J. Bricmont, J. L. Lebowitz, C.-E. Pfister, and E. Olivieri, Non translation invariant Gibbs states with coexisting phases,Commun. Math. Phys. 66:1 (1979).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ruiz, J. Interface sharpness in the Potts model. J Stat Phys 56, 621–629 (1989). https://doi.org/10.1007/BF01016770

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01016770

Key words

Navigation