The random-walk representation of classical spin systems and correlation inequalities - II. The skeleton inequalities

David C. Brydges, Jürg Fröhlich, Alan D. Sokal

    Research output: Contribution to journalArticle


    We use the random-walk representation to prove the first few of a new family of correlation inequalities for ferromagnetic φ{symbol}4 lattice models. These inequalities state that the finite partial sums of the propagator-resummed perturbation expansion for the 4-point function form an alternating set of rigorous upper and lower bounds for the exact 4-point function. Generalizations to 2 n-point functions are also given. A simple construction of the continuum φ{symbol}d4 quantum field theory (d<4), based on these inequalities, is described in a companion paper.

    Original languageEnglish (US)
    Pages (from-to)117-139
    Number of pages23
    JournalCommunications In Mathematical Physics
    Issue number1
    StatePublished - Mar 1 1983


    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics

    Cite this