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

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

    Research output: Contribution to journalArticlepeer-review


    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)
    Issue numberC
    StatePublished - May 20 1991

    ASJC Scopus subject areas

    • Atomic and Molecular Physics, and Optics
    • Nuclear and High Energy Physics


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