Journal of Statistical Physics

, Volume 9, Issue 2, pp 145–182 | Cite as

Spontaneous staggered polarization of theF-model

  • Rodney J. Baxter


The “order parameter” of the two-dimensionalF-model, namely the spontaneous staggered polarizationP0, is derived exactly. At the critical temperatureP0 has an essential singularity, bothP0 and all its derivatives with respect to temperature vanishing.

Key words

Statistical mechanics lattice statistics critical behavior two-dimensionalF-model antiferroelectric spontaneous polarization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    F. Rys,Helv. Phys. Acta 36:537 (1963).Google Scholar
  2. 2.
    E. H. Lieb,Phys. Rev. Lett. 18:1046 (1967).Google Scholar
  3. 3.
    J. F. Nagle,J. Chem. Phys. 50:2813 (1969).Google Scholar
  4. 4.
    H. N. V. Temperley and E. H. Lieb,Proc. Roy. Soc. London A 322:251 (1971); J. F. Nagle, Critical phenomena and phase transitions, inTreatise on Solid State Chemistry, Vol. 5, Plenum, New York, to appear.Google Scholar
  5. 5.
    R. J. Baxter,J. Phys. C 6:L94 (1973).Google Scholar
  6. 6.
    E. H. Lieb,Phys. Rev. 162:162 (1967).Google Scholar
  7. 7.
    R. J. Baxter,Ann. Phys. 70:193 (1972).Google Scholar
  8. 8.
    I. S. Gradshteyn and I. M. Ryzhik,Tables of Integrals, Series and Products, Academic, New York (1965).Google Scholar
  9. 9.
    R. J. Baxter,Stud. Appl. Math. 50:51 (1971).Google Scholar
  10. 10.
    E. C. Titchmarsh,Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford (1948), Section 2.8.Google Scholar
  11. 11.
    M. L. Glasser, D. B. Abraham, and E. H. Lieb,J. Math. Phys. 13:887 (1972).Google Scholar
  12. 12.
    R. J. Baxter,J. Stat. Phys. 8:25 (1973).Google Scholar
  13. 13.
    J. D. Johnson, S. Krinsky, and B. M. McCoy,Phys. Rev. Lett. 29:492 (1972).Google Scholar
  14. 14.
    B. Widom,J. Chem. Phys. 43:3892, 3898 (1965).Google Scholar
  15. 15.
    M. E. Fisher,Rep. Progr. Phys. 30:615 (1970).Google Scholar
  16. 16.
    T. D. Schultz, D. C. Mattis, and E. H. Lieb,Rev. Mod. Phys. 36:856 (1964).Google Scholar
  17. 17.
    C. N. Yang,Phys. Rev. 85:808 (1952).Google Scholar
  18. 18.
    M. Gaudin,J. Math. Phys. 12:1674, 1677 (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • Rodney J. Baxter
    • 1
  1. 1.Research School of Physical SciencesThe Australian National UniversityCanberraAustralia

Personalised recommendations