Skip to main content
Log in

Large deviations for the 2D ising model: A lower bound without cluster expansions

Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We show that a lower large-deviation bound for the block-spin magnetization in the 2D Ising model can be pushed all the way forward toward its correct “Wulff” value for all β>βc.

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.

Institutional subscriptions

References

  1. D. B. Abraham, Surface structures and phase transitions—Exact results, inPhase Transitions and Critical Phenomena, Vol. 10, C. Domb and J. L. Leibowitz, eds. (Academic Press, London, 1987), pp. 1–74.

    Google Scholar 

  2. N. Akutsu and Y. Akutsu, Relationship between the anisotropic interface tension, the scaled interface width and the equilibrium shape in two dimensions,J. Phys. A: Math. Gen. 2813–2820 (1986).

  3. J. E. Avron, H. van Beijeren, L. S. Schulman, and R. K. P. Zia, Roughening transition, surface tension and equilibrium droplet shapes in a two-dimensional Ising system,J. Phys. A: Math. Gen. 15:L81–86 (1982).

    Google Scholar 

  4. M. Aizenman, J. T. Chayes, L. Chayes, and C. M. Newman, Discontinuity of the magnetization in one=dimensional 1/|x−y|2 Ising and Potts models,J. Stat. Phys. 50:1–40 (1988).

    Google Scholar 

  5. J. T. Chayes, L. Chayes, and R. M. Schonman, Exponential decay of connectivities in the two-dimensional Ising model,J. Stat. Phys. 49:433–445 (1987).

    Google Scholar 

  6. R. L. Dobrushin, R. Kotecky, and S. Shlosman,Wulff Construction: A Global Shape from Local Interaction (AMS, Providence, Rhode Island, 1992).

    Google Scholar 

  7. R. L. Dobrushin and S. Shlosman, Large and moderate deviations in the Ising model and droplet condensation, preprint (1993).

  8. R. S. Ellis,Entropy, Large Deviations and Statistical Mechanics (Springer, Berlin, 1985).

    Google Scholar 

  9. H. Föllmer and M. Ort, Large deviations and surface entropy for Markov fields,Astérisque 157–158:173–190 (1988).

    Google Scholar 

  10. C. M. Newman, Private communication (1993).

  11. C. M. Newman, Normal fluctuations and the FKG inequalities,Commun. Math. Phys. 74:119–128 (1980).

    Google Scholar 

  12. C. E. Pfister, Large deviations and phase separation in the two-dimensional Ising model,Helv. Phys. Acta 64:953–1054 (1991).

    Google Scholar 

  13. R. T. Rockafellar,Convex Analysis (University Press, 1972).

  14. R. H. Schonmann, Second order large deviation estimates for ferromagnetic system in the phase coexistence region,Commun. Math. Phys. 112:409–422 (1987).

    Google Scholar 

  15. S. B. Shlosman, The droplet in the tube: A case of phase transition in the canonical ensemble,Commun. Math. Phys. 125:81–90 (1989).

    Google Scholar 

  16. S. B. Shlosman, Correlation inequalities and their applications,J. Sov. Math. 15:79–101 (1981).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ioffe, D. Large deviations for the 2D ising model: A lower bound without cluster expansions. J Stat Phys 74, 411–432 (1994). https://doi.org/10.1007/BF02186818

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02186818

Key Words

Navigation