The GHS and other correlation inequalities for a class of even ferromagnets |
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| Authors: | Richard S Ellis James L Monroe Charles M Newman |
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| Institution: | (1) Department of Mathematics, Northwestern University, Evanston, Illinois, USA;(2) Department of Physics, Northwestern University, Evanston, Illinois, USA;(3) Department of Mathematics, Indiana University, Bloomington, Indiana, USA;(4) Present address: Department of Mathematics, University of Massachusetts, 01002 Amherst, MA, USA;(5) Present address: Department of Chemistry, State University of New York, 11794 Stony Brook, N.Y., USA;(6) Present address: Departments of Mathematics and Physics, Technion, Haifa, Israel |
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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,  4 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.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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