Skip to main content
Log in

Surface Transitions of the Semi-Infinite Potts Model I: The High Bulk Temperature Regime

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

Abstract

We propose a rigorous approach of Semi-Infinite lattice systems illustrated with the study of surface transitions of the semi-infinite Potts model.

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. D. B. Abraham, Surface structures and phase transitions-exact results, in Phases Transitions and Critical Phenomena, Vol. 10, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, New York, 1986).

    Google Scholar 

  2. P. S. Aleksandrov, Combinatorial Topology, Vol. 3 (Graylock Press, Albany, 1960).

    Google Scholar 

  3. K. Binder, Critical behaviour at surfaces, in Phases Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, New York, 1983).

    Google Scholar 

  4. C. Borgs and J. Imbrie, A unified approach to phase diagrams in fields theory and statistical mechanics, Commun. Math. Phys. 123:305(1989).

    Google Scholar 

  5. A. Bakchich, A. Benyoussef, and L. Laanait, Phase diagram of the Potts model in an external magnetic field, Ann. Inst. Henri Poincaré 50:17(1989).

    Google Scholar 

  6. J. Bricmont, K. Kuroda, and J. L. Lebowitz, First order phase transitions in lattice and continuous systems, Commun. Math. Phys. 101:501–538 (1985).

    Google Scholar 

  7. F. Cesi and F. Martinelli, On the layering transition of an SOS model interacting with a wall I. Equilibrium results, J. Stat. Phys. 82, 823(1997).

    Google Scholar 

  8. R. L. Dobrushin, Estimates of semi-invariants for the Ising model at low temperatures, Amer. Math. Soc. Transl. 177:59(1996).

    Google Scholar 

  9. E. I. Dinaburg and A. E. Mazel, Layering transition in SOS model with external magnetic field, J. Stat. Phys. 74:533(1994).

    Google Scholar 

  10. E. I. Dinaburg and Ya. G. Sinai, Tr. Conf. Mat. Fiz. (1984); and Selecta. Math. Sov. 7:3 (1987).

  11. R. L. Dobrushin, R. Kotecky, and S. Shlosman, Wulff Construction: A Global Shape from Local Interactions (Providence, 1992).

  12. K. Druhl and H. Wagner, Algebraic formulation of duality transformation for abelian lattice model, Ann. Phys. 141:225(1982).

    Google Scholar 

  13. G. Gallavotti, A. Martin Lö;f, and S. Miracle-Solé, Some problems connected with the coexistence of phases in the Ising model, in Statistical Mechanics and Mathematical Problems, Lecture Notes in Physics, Vol. 20, (Springer, Berlin, 1973), p. 162.

    Google Scholar 

  14. C. M. Fortuin and P. W. Kasteleyn, On the random-cluster model I: Introduction and relation to other models, Physica 57:536(1972).

    Google Scholar 

  15. J. Frö;hlich and C. E. Pfister, Semi-infinite Ising model I: Thermodynamic functions and phase diagram in absence of magnetic field, Commun. Math. Phys. 109:493(1987).

    Google Scholar 

  16. J. Frö;hlich and C. E. Pfister, Semi-infinite Ising model II: The wetting and layering transition, Commun. Math. Phys. 112:51(1987).

    Google Scholar 

  17. J. Frö;hlich and C. E. Pfister, The wetting and layering transitions in the half-infinite Ising model, Europhys. Lett. 3:845(1987).

    Google Scholar 

  18. P. Holicky, R. Kotecky, and M. Zahradnik, Rigid interfaces for lattice models at low temperatures, J. Stat. Phys. 50:755(1988).

    Google Scholar 

  19. R. Kotecky, L. Laanait, A. Messager, and J. Ruiz, The q‐;state Potts model in the standard Pirogov-Sinai theory: surface tension and Wilson loops, J. Stat. Phys. 58:199(1990).

    Google Scholar 

  20. R. Koteck´y and D. Preiss, Cluster expansion for abstract polymer models, Commun. Math. Phys. 103:491(1986).

    Google Scholar 

  21. R. Koteck´y and D. Preiss, An inductive approach to Pirogov-Sinai theory, Supp. Rend. Circ. Matem. Palermo II 3:161(1984).

    Google Scholar 

  22. L. Laanait, N. Masaif, and J. Ruiz, Phase coexistence in partially symmetric q‐;state models, J. Stat. Phys. 72:721(1993).

    Google Scholar 

  23. L. Laanait, A. Messager, and J. Ruiz, Phase coexistence and surface tensions for the Potts model, Commun. Math. Phys. 105:527(1986).

    Google Scholar 

  24. L. Laanait, A. Messager, S. Miracle-Sole, J. Ruiz, and S. Shlosman, Interfaces the in Potts model I: Pirogov-Sinai theory of the Fortuin-Kasteleyn representation, Commun. Math. Phys. 140:81(1991).

    Google Scholar 

  25. S. Lefschetz, Introduction to Topology (Princeton University Press, Princeton, 1949).

    Google Scholar 

  26. R. Lipowsky, The Semi-infinite Potts model: A new low temperature phase, Z. Phys. B-Condenced Matter 45:229(1982).

    Google Scholar 

  27. S. Miracle-Solé, On the convergence of cluster expansion, Physica A 279:244(2000).

    Google Scholar 

  28. B. M. Mc Coy and T. T. Wu, The two-dimensional Ising model (Harvard University Press, Cambridge, MA, 1973).

    Google Scholar 

  29. C. E. Pfister and O. Penrose, Analyticity properties of the surface free energy of the Ising model, Commun. Math. Phys. 115:691(1988).

    Google Scholar 

  30. O. Ore, The Four-Color Problem (Academic Press, New York, London, 1967).

    Google Scholar 

  31. D. Ruelle, Statistical Mechanics: Rigorous Results (Benjamin, New York, Amsterdam, 1969).

    Google Scholar 

  32. Ya. G. Sinai, Theory of Phase Transitions: Rigorous Results (Pergamon Press, London, 1982).

    Google Scholar 

  33. A. D. Sokal, Bounds on the complex zeros of (Di)chromatics polynomials and Potts-model partitions functions, Combinatorics, Probability, and Computing 10:41(2001).

    Google Scholar 

  34. M. Zahradnik, An alternate version of Pirogov-Sinai theory, Commun. Math. Phys. 93:359(1984).

    Google Scholar 

  35. M. Zahradnik, Analyticity of low-temperature phase diagram of lattice spin models, J. Stat. Phys. 47:725(1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dobrovolny, C., Laanait, L. & Ruiz, J. Surface Transitions of the Semi-Infinite Potts Model I: The High Bulk Temperature Regime. Journal of Statistical Physics 114, 1269–1302 (2004). https://doi.org/10.1023/B:JOSS.0000013957.89983.81

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:JOSS.0000013957.89983.81

Navigation