Skip to main content
Log in

A class of interaction-round-a-face models and its equivalence with an ice-type model

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

Abstract

A new model (called the Temperley-Lieb interactions model) is introduced, in two-dimensional lattice statistics, on a square lattice ℒ. The Temperley-Lieb equivalence of this model to the six-vertex, self-dual Potts, critical hard-hexagons and critical nonintersecting string models is established. A graphical equivalence of this model to the six-vertex model generalizes this equivalence to noncritical cases of the above models. The order parameters of a specialization of this model are studied.

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. C. L. Schultz,Phys. Rev. Lett. 46:629 (1981).

    Google Scholar 

  2. H. N. V. Temperley and E. H. Lieb,Proc. R. Soc. Lond. A 322:251 (1971).

    Google Scholar 

  3. R. J. Baxter,J. Stat. Phys. 28:1 (1982).

    Google Scholar 

  4. J. H. H. Perk and C. L. Schultz,Physica 122A:50 (1983).

    Google Scholar 

  5. R. J. Baxter, S. B. Kelland, and F. Y. Wu,J. Phys. A 9:397 (1976).

    Google Scholar 

  6. J. H. H. Perk and F. Y. Wu,J. Stat. Phys. 42:727 (1986).

    Google Scholar 

  7. T. T. Truong,J. Stat. Phys. 42:349 (1986).

    Google Scholar 

  8. J. H. H. Perk and F. Y. Wu,Physica 138A:100 (1986).

    Google Scholar 

  9. R. J. Baxter,J. Phys. C 6:445 (1973).

    Google Scholar 

  10. R. J. Baxter,Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982).

    Google Scholar 

  11. R. B. Potts,Proc. Camb. Phil. Soc. 48:106 (1952).

    Google Scholar 

  12. P. A. Pearce,J. Phys. A 18:3217 (1985).

    Google Scholar 

  13. A. L. Owczarek and R. J. Baxter,J. Phys. A 20:5263 (1987).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Owczarek, A.L., Baxter, R.J. A class of interaction-round-a-face models and its equivalence with an ice-type model. J Stat Phys 49, 1093–1115 (1987). https://doi.org/10.1007/BF01017562

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01017562

Key words

Navigation