Shapes, Surfaces, and Interfaces in Percolation Clusters View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

1985

AUTHORS

Antonio Coniglio

ABSTRACT

Percolation theory is reviewed. Intuitive arguments are given to derive scaling and hyperscaling relations. Above six dimensions the breakdown of hyperscaling is related to the interpenetration of the critical large clusters, and to the appearence at pc of an infinite number of infinite clusters of zero density with fractal dimension df = 4. The structure of the percolating cluster made of links and blobs is characterized by an infinite set of exponents related to the anomalous voltage distribution in a random resistor network at pc. The surface structure of critical clusters below pc, which is relevant to the study of random superconducting networks, is also discussed. In particular, an exact result is presented which shows that in any dimension the interface of two critical clusters diverge as (pc-p)-1 as the percolation threshold is approached. More... »

PAGES

84-101

Book

TITLE

Physics of Finely Divided Matter

ISBN

978-3-642-93303-5
978-3-642-93301-1

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/978-3-642-93301-1_11

DOI

http://dx.doi.org/10.1007/978-3-642-93301-1_11

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048022141


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