Mean Field Theory, Ginzburg Criterion, and Marginal Dimensionality of Phase-Transitions

Jens Aage Als-Nielsen, R. J. Birgenau

    Research output: Contribution to journalJournal articleResearchpeer-review


    By applying a real space version of the Ginzburg criterion, the role of fluctuations and thence the self‐consistency of mean field theory are assessed in a simple fashion for a variety of phase transitions. It is shown that in using this approach the concept of ’’marginal dimensionality’’ emerges in a natural way. For example, it is shown that for many homogeneous structural transformations the marginal dimensionality is two, so that mean field theory will be valid for real three‐dimensional systems. It is suggested that this simple self‐consistent approach to Landau theory should be incorporated in the teaching of elementary phase transition phenomena.
    Original languageEnglish
    JournalAmerican Journal of Physics
    Issue number6
    Pages (from-to)554-560
    Publication statusPublished - 1977


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