On the equivalence of different order parameters for Ising ferromagnets

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In a recent note Barber showed, for a spin-1/2 Ising system with ferromagnetic pair interactions, that some critical exponents of the "triplet order parameter" 〈σiσjσk〉 are the same as those of the magnetization 〈σi〉. Here we prove such results for all odd correlations and dispense with the requirement of pair interactions. We also prove that the critical temperature Tc, defined as the temperature below which there is a spontaneous magnetization, is for fixed "even" spin interactions Je independent of the way in which the "odd" interactions Jo approach zero from "above." This is achieved by using only the "simplest," Griffiths-Kelley-Sherman (GKS), inequalities, which apply to the most general many-spin, ferromagnetic interactions.

Original languageEnglish (US)
Pages (from-to)3-9
Number of pages7
JournalJournal of Statistical Physics
Issue number1
StatePublished - Jan 1977
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


  • Ising ferromagnets
  • critical exponents
  • different order parameters
  • inequalities


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