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

    Abstract

    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}d 4 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
    Volume91
    Issue number1
    DOIs
    StatePublished - Mar 1983

    Fingerprint

    Correlation Inequalities
    Spin Systems
    Skeleton
    musculoskeletal system
    random walk
    Random walk
    Perturbation Expansion
    Partial Sums
    Propagator
    Lattice Model
    Quantum Field Theory
    Upper and Lower Bounds
    Continuum
    continuums
    perturbation
    expansion
    propagation

    ASJC Scopus subject areas

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

    Cite this

    The random-walk representation of classical spin systems and correlation inequalities - II. The skeleton inequalities. / Brydges, David C.; Fröhlich, Jürg; Sokal, Alan D.

    In: Communications in Mathematical Physics, Vol. 91, No. 1, 03.1983, p. 117-139.

    Research output: Contribution to journalArticle

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