Skip to main content

Internal energy density of the critical three-state Potts model on the kagome lattice

Abstract

The internal energy density of the Potts model on a semi-infinite strip with a width L has been conjectured to have no finite-size corrections at the critical point K = K c . By factorizing the transfer matrix for the kagome lattice with larger widths, we have found that this conjecture is not correct in that the internal energy density varies slightly with L at the critical point. From this size dependence of the internal energy density, we obtain an upper bound as K c < 1.0565615, which is close to a recent estimate K JS c = 1.0565600(7) by Jacobsen and Scullard [J. Phys. A 45, 494003 (2012)]. We also obtain a lower bound as K c > 1.0560 by calculating the correlation length along the strips.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).

    ADS  Article  Google Scholar 

  2. [2]

    R. M. Ziff and P. N. Suding, J. Phys. A 30, 5351 (1997).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  3. [3]

    I. Jensen, A. J. Guttmann and I. G. Enting, J. Phys. A 30, 8067 (1997).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  4. [4]

    S. K. Baek, H. Mäkelä, P. Minnhagen and B. J. Kim, Phys. Rev. E 83, 061104 (2011).

    ADS  Article  Google Scholar 

  5. [5]

    J. Wosiek, Phys. Rev. B 49, 15023 (1994).

    ADS  Article  Google Scholar 

  6. [6]

    H. W. J. Blöte and M. P. Nightingale, Physica A 112, 405 (1982).

    MathSciNet  ADS  Article  Google Scholar 

  7. [7]

    H. W. J. Blöte and B. Nienhuis, J. Phys. A 22, 1415 (1989).

    MathSciNet  ADS  Article  Google Scholar 

  8. [8]

    D. P. Foster, C. Gérard and I. Puha, J. Phys. A 34, 5183 (2001).

    MathSciNet  ADS  Article  MATH  Google Scholar 

  9. [9]

    J. L. Jacobsen and C. R. Scullard, J. Phys. A 45, 494003 (2012).

    MathSciNet  Article  Google Scholar 

  10. [10]

    J. Cardy, J. Phys. A 17, L385 (1984).

    MathSciNet  ADS  Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Seung Ki Baek.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Baek, S.K., Mäkelä, H. Internal energy density of the critical three-state Potts model on the kagome lattice. Journal of the Korean Physical Society 63, 1167–1170 (2013). https://doi.org/10.3938/jkps.63.1167

Download citation

Keywords

  • Potts model
  • Kagome lattice