Hyperscaling above the upper critical dimension

B. Berche, Ralph Kenna, J-C. Walter

    Research output: Contribution to journalArticlepeer-review

    46 Citations (Scopus)


    Above the upper critical dimension, the breakdown of hyperscaling is associated with dangerous irrelevant variables in the renormalization group formalism at least for systems with periodic boundary conditions. While these have been extensively studied, there have been only a few analyses of finite-size scaling with free boundary conditions. The conventional expectation there is that, in contrast to periodic geometries, finite-size scaling is Gaussian, governed by a correlation length commensurate with the lattice extent. Here, detailed numerical studies of the five-dimensional Ising model indicate that this expectation is unsupported, both at the infinite-volume critical point and at the pseudocritical point where the finite-size susceptibility peaks. Instead the evidence indicates that finite-size scaling at the pseudocritical point is similar to that in the periodic case. An analytic explanation is offered which allows hyperscaling to be extended beyond the upper critical dimension.
    Original languageEnglish
    Pages (from-to)115-132
    JournalNuclear Physics B
    Issue number1
    Publication statusPublished - 2012

    Bibliographical note

    The full text of this item is not available from the repository.


    • hyperscaling
    • upper critical dimension
    • finite-size scaling
    • free boundary conditions


    Dive into the research topics of 'Hyperscaling above the upper critical dimension'. Together they form a unique fingerprint.

    Cite this