Communications in Mathematical Physics

, Volume 46, Issue 2, pp 167–182 | Cite as

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

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


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.


Neural Network Statistical Physic Field Theory Complex System Quantum Field Theory 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Richard S. Ellis
    • 1
  • James L. Monroe
    • 2
  • Charles M. Newman
    • 3
  1. 1.Department of MathematicsNorthwestern UniversityEvanstonUSA
  2. 2.Department of PhysicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of MathematicsIndiana UniversityBloomingtonUSA

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