Correlations in Thermal & Geometrical Systems View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1990

AUTHORS

Antonio Coniglio

ABSTRACT

It is shown how correlations in spin systems can be described in terms of geometrical clusters. For the q-state Potts model exact relations are given between connectivity and thermal properties. A cluster dynamics developed by Swendsen and Wang is described. At criticality these clusters are shown to have a fractal structure made of links and blobs as in percolation. In two dimensions the value of the fractal dimension of the links or red bonds and the fractal dimension of the hull of the incipient infinite cluster can be found exactly for all values of 0 ≤ q ≤ 4. Extension of these geometrical concepts to Ising spin glasses is also made. The clusters now represent fluctuations which interfere with each other and give rise to net correlations which are shorter than the typical cluster radius. In fact it is found numerically that the mean cluster size diverges well above the spin glass transition. More... »

PAGES

21-33

References to SciGraph publications

  • 1990-02. Fractal dimension of 3D Ising droplets in ZEITSCHRIFT FÜR PHYSIK B CONDENSED MATTER
  • Book

    TITLE

    Correlations and Connectivity

    ISBN

    978-0-7923-1011-2
    978-94-009-2157-3

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-009-2157-3_2

    DOI

    http://dx.doi.org/10.1007/978-94-009-2157-3_2

    DIMENSIONS

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