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The GHS and other correlation inequalities for a class of even ferromagnets

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Abstract

We prove the GHS inequality for families of random variables which arise in certain ferromagnetic models of statistical mechanics and quantum field theory. These include spin −1/2 Ising models, ϕ4 field theories, and other continuous spin models. The proofs are based on the properties of a classG − of probability measures which contains all measures of the form const exp(−V(x))dx, whereV is even and continuously differentiable anddV/dx is convex on [0, ∞). A new proof of the GKS inequalities using similar ideas is also given.

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Author notes

  1. Richard S. Ellis

    Present address: Department of Mathematics, University of Massachusetts, 01002, Amherst, MA, USA

  2. James L. Monroe

    Present address: Department of Chemistry, State University of New York, 11794, Stony Brook, N.Y., USA

  3. Charles M. Newman

    Present address: Departments of Mathematics and Physics, Technion, Haifa, Israel

Authors and Affiliations

  1. Department of Mathematics, Northwestern University, Evanston, Illinois, USA

    Richard S. Ellis

  2. Department of Physics, Northwestern University, Evanston, Illinois, USA

    James L. Monroe

  3. Department of Mathematics, Indiana University, Bloomington, Indiana, USA

    Charles M. Newman

Authors
  1. Richard S. Ellis
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  2. James L. Monroe
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  3. Charles M. Newman
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Additional information

Communicated by G. Gallavotti

Supported in part by National Science Foundation Grant MPS 71-02838 A 04.

Supported by National Science Foundation Grant MPS 74-24696.

Supported in part by National Science Foundation Grant MPS 74-04870.

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Ellis, R.S., Monroe, J.L. & Newman, C.M. The GHS and other correlation inequalities for a class of even ferromagnets. Commun.Math. Phys. 46, 167–182 (1976). https://doi.org/10.1007/BF01608495

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  • DOI: https://doi.org/10.1007/BF01608495

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