Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2014-06

AUTHORS

F. Antenucci, A. Crisanti, L. Leuzzi

ABSTRACT

Renormalization group based on the Migdal–Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical models. In presence of quenched disorder, however, predictions obtained with the Migdal–Kadanoff bond removal approach quite often fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In an attempt to overcome this limitation we analyze the behavior of Ising and Blume–Emery–Griffiths models on more structured hierarchical lattices. We find that, apart from some exceptions, the failure is not limited to Midgal–Kadanoff cells but originates right from the hierarchization of Bravais lattices on small cells, and shows up also when in-cell loops are considered. More... »

PAGES

909-931

References to SciGraph publications

  • 1987. Scaling theory of the ordered phase of spin glasses in HEIDELBERG COLLOQUIUM ON GLASSY DYNAMICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10955-014-0977-z

    DOI

    http://dx.doi.org/10.1007/s10955-014-0977-z

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1035019196


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