Skip to main content
Log in

Interfacial free energy of the two-dimensional Ising model from the renormalization group

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

Abstract

The interfacial free energy of a two-dimensional Ising model is calculated by using various renormalization group schemes. The results obtained are quantitatively consistent with known exact results. In addition, a general discussion of various drawbacks within different renormalization group approximations is given. The best result are obtained with the 4×4 finite cluster approximation, while the Migdal-Kadanoff approximation seems to be inherently unsuitable for calculation of interfacial properties.

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. M. Wortis, inFundamtental Problems in Statistical Mechanics VI, D. Cohen, ed. (North-Holland, Amsterdam, 1985), p. 87.

    Google Scholar 

  2. R. B. Griffiths, inPhase Transitions in Surface Films, J. G. Dash and J. Ruvals, eds. (Plenum Press, New York, 1980), p. 1.

    Google Scholar 

  3. L. D. Landau and E. M. Lifshitz,Statistical Physics (Pergamon, London, 1959).

    Google Scholar 

  4. C. Domb and M. S. Green, eds.,Phase Transitions and Critical Phenomena, Vol. 3 (Academic Press, London, 1974).

    Google Scholar 

  5. K. Binder, inPhase Transitions and Critical Phenomena, Vol. 8, C. Domb and J. L. Lebowitz, eds. (Academic Press, London, 1983), p. 1.

    Google Scholar 

  6. M. Nauenberg and. Nienhuis,Phys. Rev. Lett. 33:1598 (1974).

    Google Scholar 

  7. K. Binder,Phys. Rev. A 25:1699 (1982).

    Google Scholar 

  8. E. Bürkner and D. Stauffer,Z. Phys. B 53:241 (1983).

    Google Scholar 

  9. K. K. Mon and D. Jasnow,Phys. Rev. A 30:670 (1984).

    Google Scholar 

  10. K. K. Mon and D. Jasnow,Phys. Rev. A 31:4008 (1985).

    Google Scholar 

  11. D. B. Abraham and N. M. Švrakić,Phys. Rev. Lett. 56:1172 (1986).

    Google Scholar 

  12. J. D. Weeks, inOrdering in Strongly Fluctuating Condensed Matter Systems, T. Riste, ed. (Plenum Press, New York, 1980), p. 293.

    Google Scholar 

  13. M. J. de Oliveira, D. Furman, and R. B. Griffiths,Phys. Rev. Lett. 40:977 (1978).

    Google Scholar 

  14. T. W. Burkhardt and J. M. J. van Leeuwen, eds.,Real-Space Renormalization (Springer-Verlag, Berlin, 1982).

    Google Scholar 

  15. T. Niemeyer and J. M. J. van Leeuwen,Physica 71:17 (1974).

    Google Scholar 

  16. L. P. Kadanoff,Ann. Pys. (N.Y.)100:359 (1976).

    Google Scholar 

  17. N. M. Švrakić, R. Pandit, and M. Wortis,Phys. Rev. B 22:1286 (1980).

    Google Scholar 

  18. L. Onsager,Phys. Rev. 65:117 (1944).

    Google Scholar 

  19. D. B. Abraham,Phys. Rev. Lett. 44:1165 (1980).

    Google Scholar 

  20. D. B. Abraham,J. Phys. A 14:L369 (1981).

    Google Scholar 

  21. J. D. Weeks, G. H. Gilmer, and H. J. Leamy,Phys. Rev. Lett. 31:549 (1973).

    Google Scholar 

  22. B. Widom, inPhase Transitions and Critical Phenomena, Vol. 2, C. Domb and M. S. Green, eds. (Academic Press, London, 1972), p. 79.

    Google Scholar 

  23. W. Klein, D. J. Wallace, and R. K. Zia,Phys. Rev. Lett. 37:639 (1976).

    Google Scholar 

  24. S. Hsu and J. D. Gunton,Phys. Rev. B 15:2688 (1977).

    Google Scholar 

  25. N. M. Švrakić,J. Phys. A 16:L171 (1983).

    Google Scholar 

  26. T. W. Burkhardt and E. Eisenriegler,Phys. Rev. B 16:3213 (1977).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bilalbegović, G., Švrakić, N.M. Interfacial free energy of the two-dimensional Ising model from the renormalization group. J Stat Phys 46, 777–787 (1987). https://doi.org/10.1007/BF01013385

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01013385

Key words

Navigation