Skeleton inequalities and mean field properties for lattice spin systems

Takashi Hara, Tetsuya Hattori, Hal Tasaki

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Abstract

We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ2) = (a/2)φ2 + Σn = 2M2n/(2n)!} φ2n (a real, λ2n ≥0) generalizing the Brydges-Fröhlich-Sokal and Bovier-Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d > 4 dimensions, critical exponents γ, α, and Δ4 take their mean-field values (i.e., γ = 1, α = 0, and Δ4 = 3/2).

Original languageEnglish
Pages (from-to)2922-2929
Number of pages8
JournalJournal of Mathematical Physics
Volume26
Issue number11
DOIs
Publication statusPublished - 1985 Jan 1

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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