More inequalities for critical exponents

Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review

    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

    Keywords

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

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

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