More surprises in the general theory of lattice systems

Alan D. Sokal

    Research output: Contribution to journalArticlepeer-review


    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
    Issue number3
    StatePublished - Sep 1982

    ASJC Scopus subject areas

    • Statistical and Nonlinear Physics
    • Mathematical Physics


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