Journal of Statistical Physics

, Volume 19, Issue 5, pp 461–478 | Cite as

Variational approximations for square lattice models in statistical mechanics

  • R. J. Baxter


This paper concerns a square lattice, Ising-type model with interactions between the four spins at the corners of each face. These may include nearest and next-nearest-neighbor interactions, and interactions with a magnetic field. Provided the Hamiltonian is symmetric with respect to both row reversal and column reversal, a rapidly convergent sequence of variational approximations is obtained, giving the free energy and other thermodynamic properties. For the usual Ising model, the lowest such approximations are those of Bethe and of Kramers and Wannier. The method provides a new definition of corner transfer matrices.

Key words

Statistical mechanics lattice statistics Ising models variational approximation corner transfer matrices 


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Copyright information

© Plenum Publishing Corporation 1978

Authors and Affiliations

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

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