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Correlations in Ising ferromagnets. III

A mean-field bound for binary correlations

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Abstract

An inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannot exhibit a spontaneous magnetization at temperatures above the mean-field approximation to the Curie or “critical” point. (As a consequence, the corresponding “lattice gas” cannot undergo a first order phase transition in density (condensation) above this temperature.) The mean-field susceptibility in zero magnetic field at high temperatures is shown to be an upper bound for the exact result.

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References

  1. Peierls, R.: Proc. Cambridge Phil. Soc.32, 477 (1936).

    Google Scholar 

  2. Griffiths, R. B.: Phys. Rev.136, A437 (1964).

    Google Scholar 

  3. Dobrushin, R. L.: Teoriya Veroyatnostei i ee Primeneniya10, 209 (1965). [English translation: Theory of Probability and its Applications10, 193 (1965)].

    Google Scholar 

  4. Ginibre, J., A. Grossman, andD. Ruelle: Commun. Math. Phys.3, 187 (1966).

    Google Scholar 

  5. Griffiths, R. B.: Phys. Rev.152, 240 (1966).

    Google Scholar 

  6. Lee, T. D., andC. N. Yang: Phys. Rev.87, 410 (1952).

    Google Scholar 

  7. Baur, M. E., andL. H. Nosanow: J. Chem. Phys.37, 153 (1962).

    Google Scholar 

  8. Mermin, N. D., andH. Wagner: Phys. Rev. Letters17, 1133, 1307 (1966).

    Google Scholar 

  9. Yang, C. N.: Phys. Rev.85, 808 (1952).

    Google Scholar 

  10. Onsager, L.: Phys. Rev.65, 117 (1944).

    Google Scholar 

  11. Schultz, T. D., D. C. Mattis, andE. H. Lieb: Rev. Mod. Phys.36, 856 (1964).

    Google Scholar 

  12. Griffiths, R. B.: J. Math. Phys.8, 478 (1967).

    Google Scholar 

  13. —— J. Math. Phys.8, 484 (1967).

    Google Scholar 

  14. Yang, C. N., andT. D. Lee: Phys. Rev.87, 404 (1952).

    Google Scholar 

  15. Griffiths, R. B.: Math. Phys.5, 1215 (1964).

    Google Scholar 

  16. Fisher, M. E.: Phys. Rev. (to be published).

  17. Kelly, D. G., andS. Sherman (to be published).

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Authors and Affiliations

  1. Physics Department, Carnegie Institute of Technology, 15213, Pittsburgh, Pennsylvania

    Robert B. Griffiths

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  1. Robert B. Griffiths
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Research supported in part by the National Science Foundation.

Alfred P. Sloan research fellow.

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Griffiths, R.B. Correlations in Ising ferromagnets. III. Commun.Math. Phys. 6, 121–127 (1967). https://doi.org/10.1007/BF01654128

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  • DOI: https://doi.org/10.1007/BF01654128

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