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

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, 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
Volume46
Issue number2
DOIs
StatePublished - Jun 1976

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Correlation Inequalities
Ferromagnet
random variables
Spin Models
Continuously differentiable
Quantum Field Theory
statistical mechanics
Statistical Mechanics
Field Theory
Ising model
Ising Model
Probability Measure
Random variable
Class
Model
Family
Form

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Physics and Astronomy(all)
  • Mathematical Physics

Cite this

The GHS and other correlation inequalities for a class of even ferromagnets. / Ellis, Richard S.; Monroe, James L.; Newman, Charles M.

In: Communications in Mathematical Physics, Vol. 46, No. 2, 06.1976, p. 167-182.

Research output: Contribution to journalArticle

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