Necessary and sufficient conditions for the ghs inequality with applications to analysis and probability

Richard S. Ellis, Charles M. Newman

Research output: Contribution to journalArticle

Abstract

The GHS inequality is an important tool in the study of the Ising model of ferromagnetism (a model in equilibrium statistical mechanics) and in Euclidean quantum field theory. This paper derives necessary and sufficient conditions on an Ising spin system for the GHS inequality to be valid. Applications to convexity-preserving properties of certain differential equations and diffusion processes are given.

Original languageEnglish (US)
Pages (from-to)83-99
Number of pages17
JournalTransactions of the American Mathematical Society
Volume237
DOIs
StatePublished - Mar 1978

Keywords

  • Convex function
  • GHS inequality
  • Ising model
  • Parabolic partial differential equation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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