Renormalization transformations in the vicinity of first-order phase transitions: What can and cannot go wrong

Aernout C.D. Van Enter, Roberto Fernandez, Alan D. Sokal

    Research output: Contribution to journalArticle


    We reconsider 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)3253-3256
    Number of pages4
    JournalPhysical Review Letters
    Issue number25
    StatePublished - Jan 1 1991


    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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