Journal of Statistical Physics

, Volume 20, Issue 1, pp 95–114 | Cite as

Square lattice variational approximations applied to the Ising model

  • S. K. Tsang


The variational method developed by Baxter is applied to the zero-field Ising model on the square lattice. The problem is simplified to that of solving a relatively small system of nonlinear equations. The estimates to the spontaneous magnetization and the critical temperature from the sequence of variational approximations are obtained. The results converge rapidly to the exact ones. They exhibit a crossover phenomenon and satisfy a scaling relation.

Key words

Ising model variational approximation spinor representatives crossover phenomena scaling 


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  1. 1.
    R. J. Baxter,J. Math. Phys. 9:650 (1968).Google Scholar
  2. 2.
    S. B. Kelland,Can. J. Phys. 54:1621 (1976).Google Scholar
  3. 3.
    R. J. Baxter,J. Stat. Phys. 19:461 (1978).Google Scholar
  4. 4.
    H. A. Kramers and G. H. Wannier,Phys. Rev. 60:263 (1941).Google Scholar
  5. 5.
    B. Kaufmann,Phys. Rev. 76:1232 (1949).Google Scholar
  6. 6.
    R. J. Baxter,J. Stat. Phys. 15:485 (1976).Google Scholar
  7. 7.
    R. J. Baxter,J. Stat. Phys. 17:1 (1977).Google Scholar
  8. 8.
    C. N. Yang,Phys. Rev. 85:808 (1952).Google Scholar
  9. 9.
    A. Hankey and H. E. Stanley,Phys. Rev. B 6:3515 (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • S. K. Tsang
    • 1
  1. 1.Research School of Physical SciencesThe Australian National UniversityCanberraAustralia

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