More surprises in the general theory of lattice systems

Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    I use Israel's methods to prove new theorems of "ubiquitous pathology" for classical and quantum lattice systems. The main result is the following: Let Φ be any interaction and ρ{variant} be any translation-invariant equilibrium state for Φ (extremal or not). Then there exists a sequence {Φk} of interactions converging to Φ, having extremal (or even unique) translation-invariant equilibrium states ρ{variant}k, such that {ρ{variant}k} converges to ρ{variant}. In certain situations the perturbations Φk-Φ can be chosen to lie in a cone of "antiferromagnetic pair interactions." I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r2 interaction (Thouless effect).

    Original languageEnglish (US)
    Pages (from-to)327-336
    Number of pages10
    JournalCommunications in Mathematical Physics
    Volume86
    Issue number3
    DOIs
    StatePublished - Sep 1982

    Fingerprint

    Lattice System
    Equilibrium State
    Enter
    Interaction
    Invariant
    Interaction Effects
    interactions
    Quantum Systems
    Israel
    Ising Model
    pathology
    Cone
    trucks
    Ising model
    Perturbation
    Converge
    cones
    theorems
    Theorem
    perturbation

    ASJC Scopus subject areas

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

    Cite this

    More surprises in the general theory of lattice systems. / Sokal, Alan D.

    In: Communications in Mathematical Physics, Vol. 86, No. 3, 09.1982, p. 327-336.

    Research output: Contribution to journalArticle

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