Journal of Statistical Physics

, Volume 15, Issue 6, pp 485–503 | Cite as

Corner transfer matrices of the eight-vertex model. I. Low-temperature expansions and conjectured properties

  • R. J. Baxter


A “corner transfer matrix” (CTM) is defined for the zero-field, eight-vertex model on the square lattice. Its logarithm and its diagonal form are obtained to second order in a perturbation expansion of low-temperature type. They turn out to have a very simple form, apart from certain “remainder” contributions that can be ignored in the limit of a large lattice. It is conjectured that in this limit the operators have these simple forms for all temperatures less than the critical temperatureTc. The spontaneous magnetization can then easily be obtained, and agrees with the expression previously proposed. It is intended to prove some of the conjectures in subsequent papers.

Key words

Lattice statistics eight-vertex model corner transfer matrices spontaneous magnetization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. J. Baxter,Ann. Phys. 70:193 (1972).Google Scholar
  2. 2.
    M. N. Barber and R. J. Baxter,J. Phys. C Solid State Phys. 6:2913 (1973).Google Scholar
  3. 3.
    R. J. Baxter and F. Y. Wu,Aust. J. Phys. 27:357 (1974).Google Scholar
  4. 4.
    R. J. Baxter, M. F. Sykes, and M. G. Watts,J. Phys. A Math. Gen. 8:245 (1975).Google Scholar
  5. 5.
    R. J. Baxter,Ann. Phys. 76:1 (1973).Google Scholar
  6. 6.
    R. J. Baxter,J. Stat. Phys. 9:145 (1973).Google Scholar
  7. 7.
    F. Y. Wu,Phys. Rev. B 4:2312 (1971).Google Scholar
  8. 8.
    L. P. Kadanoff and R. J. Wegner,Phys. Rev. B 4:3989 (1971).Google Scholar
  9. 9.
    C. N. and C. P. Yang,Phys. Rev. 150:321 (1966).Google Scholar
  10. 10.
    R. J. Baxter,Ann. Phys. 70:323 (1972).Google Scholar
  11. 11.
    C. Fan and F. Y. Wu,Phys. Rev. B 2:723 (1970).Google Scholar
  12. 12.
    I. S. Gradshteyn and I. M. Ryzhik,Table of Integrals, Series and Products (Academic Press, New York and London, 1965), §8.1.Google Scholar
  13. 13.
    D. Ruelle,Statistical Mechanics: Rigorous Results (W. A. Benjamin, New York, 1969).Google Scholar
  14. 14.
    B. Kaufman,Phys. Rev. 76:1232 (1949).Google Scholar

Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

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

Personalised recommendations