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

    Abstract

    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
    Volume66
    Issue number25
    DOIs
    StatePublished - 1991

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    interactions
    formalism

    ASJC Scopus subject areas

    • Physics and Astronomy(all)

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    Renormalization transformations in the vicinity of first-order phase transitions : What can and cannot go wrong. / Van Enter, Aernout C D; Fernandez, Roberto; Sokal, Alan D.

    In: Physical Review Letters, Vol. 66, No. 25, 1991, p. 3253-3256.

    Research output: Contribution to journalArticle

    Van Enter, Aernout C D ; Fernandez, Roberto ; Sokal, Alan D. / Renormalization transformations in the vicinity of first-order phase transitions : What can and cannot go wrong. In: Physical Review Letters. 1991 ; Vol. 66, No. 25. pp. 3253-3256.
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