Coherent-Anomaly Method in Two-Dimensional Antiferromagnetic Ising Models on Square and Triangular Lattices

  • A. Lipowski
  • M. Suzuki
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 70)


In the present paper we have applied the Coherent-Anomaly Method (CAM) [1] proposed by one of the authors (M.S.), to two-dimensional antiferromagnetic Ising models on square and triangular lattices. We determined both critical temperature T c, and critical exponent γ as functions of a uniform external magnetic field H ranging from 0 to H c. Estimations of T c and γ were based on the results obtained within the Double-Cluster Approximation (DCA). In that approximation effective fields are obtained from selfconsistency conditions imposed on correlation functions of two different clusters. We have chosen pairs of wider and wider infinite stripes, which seems to be a very appropriate choice for two-dimensional models. A partition function of a stripe can be found as the largest eigen-value of the corresponding transfer matrix. This version of the CAM has been already applied to ferromagnetic Ising models as well as to Blume-Emery-Griffiths model, and is more thoroughly described in [2,3]. Our results can be summarized as follows.


Partition Function Critical Temperature Ising Model Transfer Matrix Triangular Lattice 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • A. Lipowski
    • 1
    • 2
  • M. Suzuki
    • 1
  1. 1.Department of Physics, Faculty of ScienceUniversity of TokyoBunkyo-ku, Tokyo 113Japan
  2. 2.Department of PhysicsA. Mickiewicz UniversityPoznańPoland

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