More inequalities for critical exponents

Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequality dv′ ≥γ′+2 β ≥ 2-α′. Others are 1 ≤γ′ ≤ 1 +v′φ, 1 ≤ζ ≤ 1 δμφ, δ ≥ 1, dμφ ≥ 1 + 1/δ (for φ ≥d), dv′φ, ≥ Δ′3 + α (for φ ≥d), Δ4 ≥γ, and Δ2m ≤ Δ2m+2 (for m ≥ 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.

    Original languageEnglish (US)
    Pages (from-to)25-50
    Number of pages26
    JournalJournal of Statistical Physics
    Volume25
    Issue number1
    DOIs
    StatePublished - May 1981

    Fingerprint

    Critical Exponents
    exponents
    Ising model
    Ising Model
    Nearest Neighbor
    Vary
    Interaction
    interactions

    Keywords

    • correlation inequalities
    • Critical exponents
    • critical-exponent inequalities
    • Josephson inequality

    ASJC Scopus subject areas

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

    Cite this

    More inequalities for critical exponents. / Sokal, Alan D.

    In: Journal of Statistical Physics, Vol. 25, No. 1, 05.1981, p. 25-50.

    Research output: Contribution to journalArticle

    Sokal, Alan D. / More inequalities for critical exponents. In: Journal of Statistical Physics. 1981 ; Vol. 25, No. 1. pp. 25-50.
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