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Journal of Statistical Physics

, Volume 15, Issue 4, pp 327–341 | Cite as

Inequalities for continuous-spin Ising ferromagnets

  • Garrett S. Sylvester
Articles

Abstract

We investigate correlation inequalities for Ising ferromagnets with continuous spins, giving a simple unified derivation of inequalities of Griffiths, Ginibre, Percus, Lebowitz, and Ellis and Monroe. The single-spin measure and Hamiltonian for which an inequality may be proved become more restricted as the inequality becomes more complex. However, all results hold for a model with ferromagnetic pair interactions, positive (nonuniform) external field, and single-spin measureν eitherv(σ) = [1/(l + 1)] xΣf=0/lδ(−l +2j +σ) (spinl/2) ordv(σ) = exp [−P(σ)], whereP is an even polynomial all of whose coefficients must be positive except the quadratic, which is arbitrary. The Lebowitz correlation inequality is a corollary of the Ellis-Monroe inequality. As an application, we generalize the method of van Beijeren to establish a sharp phase interface at low temperature in nearest neighbor ferromagnets of at least three dimensions with arbitrary (symmetric) single-spin measure.

Key words

Ising model ferromagnetic correlation inequality 

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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Garrett S. Sylvester
    • 1
  1. 1.Belfer Graduate School of ScienceYeshiva UniversityNew York

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