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

Richard S. Ellis, James L. Monroe, Charles M. Newman

Research output: Contribution to journalArticle


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, φ{symbol}4 field theories, and other continuous spin models. The proofs are based on the properties of a class G- of probability measures which contains all measures of the form const exp(-V(x))dx, where V is even and continuously differentiable and dV/dx is convex on [0, ∞). A new proof of the GKS inequalities using similar ideas is also given.

Original languageEnglish (US)
Pages (from-to)167-182
Number of pages16
JournalCommunications In Mathematical Physics
Issue number2
StatePublished - Jun 1 1976


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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