Journal of the Korean Physical Society

, Volume 63, Issue 6, pp 1167–1170 | Cite as

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



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 c JS = 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.


Potts model Kagome lattice 


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  1. [1]
    F. Y. Wu, Rev. Mod. Phys. 54, 235 (1982).ADSCrossRefGoogle Scholar
  2. [2]
    R. M. Ziff and P. N. Suding, J. Phys. A 30, 5351 (1997).MathSciNetADSCrossRefMATHGoogle Scholar
  3. [3]
    I. Jensen, A. J. Guttmann and I. G. Enting, J. Phys. A 30, 8067 (1997).MathSciNetADSCrossRefMATHGoogle Scholar
  4. [4]
    S. K. Baek, H. Mäkelä, P. Minnhagen and B. J. Kim, Phys. Rev. E 83, 061104 (2011).ADSCrossRefGoogle Scholar
  5. [5]
    J. Wosiek, Phys. Rev. B 49, 15023 (1994).ADSCrossRefGoogle Scholar
  6. [6]
    H. W. J. Blöte and M. P. Nightingale, Physica A 112, 405 (1982).MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    H. W. J. Blöte and B. Nienhuis, J. Phys. A 22, 1415 (1989).MathSciNetADSCrossRefGoogle Scholar
  8. [8]
    D. P. Foster, C. Gérard and I. Puha, J. Phys. A 34, 5183 (2001).MathSciNetADSCrossRefMATHGoogle Scholar
  9. [9]
    J. L. Jacobsen and C. R. Scullard, J. Phys. A 45, 494003 (2012).MathSciNetCrossRefGoogle Scholar
  10. [10]
    J. Cardy, J. Phys. A 17, L385 (1984).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© The Korean Physical Society 2013

Authors and Affiliations

  1. 1.Department of PhysicsPukyong National UniversityBusanKorea
  2. 2.QCD Labs, COMP Centre of Excellence, Department of Applied PhysicsAalto UniversityAALTOFinland

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