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Correlation inequalities for vector spin models

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Abstract

Correlation inequalities forn-vector spin models (n ⩾ 2) are reviewed. A relatively simple and unified derivation of the inequalities is achieved, using duplicate variable methods, for spin dimensionalitiesn=2 (plane rotator model),n=3 (classical Heisenberg model), andn=4. Although correlation inequalities are lacking forn > 4, new proofs are presented for the comparison inequalities relating correlations for systems with arbitrary spin dimensionality to corresponding correlations for systems with low spin dimensionality (n = 1 or 2).

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Author notes

  1. Paul A. Pearce

    Present address: Institute for Advanced Study, Princeton, New Jersey

Authors and Affiliations

  1. Physics Department, Beaver Campus, Pennsylvania State University, Monaca, Pennsylvania

    James L. Monroe

  2. Physics Department, Carnegie-Mellon University, Pittsburgh, Pennsylvania

    Paul A. Pearce

Authors
  1. James L. Monroe
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  2. Paul A. Pearce
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Additional information

Research supported by National Science Foundation under Grant DMR 76-23071.

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Monroe, J.L., Pearce, P.A. Correlation inequalities for vector spin models. J Stat Phys 21, 615–633 (1979). https://doi.org/10.1007/BF01107905

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  • DOI: https://doi.org/10.1007/BF01107905

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