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Phase diagram of the two-dimensional Ising antiferromagnet (computer-assisted proof)

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Abstract

We study the phase diagram of the Ising antiferromagnet on a square lattice in a neighbourhood of ground state critical pointsh=±4,T=0. It leads to a question about the valuea c of the critical activity of the hard-square lattice gas. Using a constructive criterion of uniqueness we prove thata c >1 and that the phase diagram of the antiferromagnet does not bulge near mentioned critical points. It is a specific feature of this work that the proof was completed with the help of a computer.

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Authors and Affiliations

  1. Institute of Information Transmission Problems, Academy of Sciences, Moscow, USSR

    R. L. Dobrushin & S. B. Shlosman

  2. Department of Mathematical Physics, Charles University, V Holešovičkách 2, CS-18000, Prague 8, Czechoslovakia

    J. Kolafa

Authors
  1. R. L. Dobrushin
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  2. J. Kolafa
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  3. S. B. Shlosman
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Communicated by Ya. G. Sinai

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Dobrushin, R.L., Kolafa, J. & Shlosman, S.B. Phase diagram of the two-dimensional Ising antiferromagnet (computer-assisted proof). Commun.Math. Phys. 102, 89–103 (1985). https://doi.org/10.1007/BF01208821

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  • DOI: https://doi.org/10.1007/BF01208821

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