Regularity properties and pathologies of position-space renormalization-group transformations

Aernout C D van Enter, Roberto Fernández, Alan D. Sokal

    Research output: Contribution to journalArticle

    Abstract

    We consider the conceptual foundations of the renormalization-group (RG) formalism. We show that the RG map, defined on a suitable space of interactions, is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the other hand, we prove in several cases that near a first-order phase transition the renormalized measure is not a Gibbs measure for any reasonable interaction. It follows that the conventional RG description of first-order transitions is not universally valid.

    Original languageEnglish (US)
    Pages (from-to)48-52
    Number of pages5
    JournalNuclear Physics B - Proceedings Supplements
    Volume20
    Issue numberC
    DOIs
    StatePublished - May 20 1991

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    pathology
    regularity
    interactions
    formalism

    ASJC Scopus subject areas

    • Nuclear and High Energy Physics

    Cite this

    Regularity properties and pathologies of position-space renormalization-group transformations. / van Enter, Aernout C D; Fernández, Roberto; Sokal, Alan D.

    In: Nuclear Physics B - Proceedings Supplements, Vol. 20, No. C, 20.05.1991, p. 48-52.

    Research output: Contribution to journalArticle

    van Enter, Aernout C D ; Fernández, Roberto ; Sokal, Alan D. / Regularity properties and pathologies of position-space renormalization-group transformations. In: Nuclear Physics B - Proceedings Supplements. 1991 ; Vol. 20, No. C. pp. 48-52.
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