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Cited by 438

The DOI matches its Crossref record; 173 of the 173 references it cites were found in a registry or an index.

Recent advances in percolation theory and its applications

Open access
Saberi, Abbas Ali·2015·Physics Reports
DOI 10.1016/j.physrep.2015.03.003
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Abstract

Percolation is the simplest fundamental model in statistical mechanics that exhibits phase transitions signaled by the emergence of a giant connected component. Despite its very simple rules, percolation theory has successfully been applied to describe a large variety of natural, technological and social systems. Percolation models serve as important universality classes in critical phenomena characterized by a set of critical exponents which correspond to a rich fractal and scaling structure of their geometric features. In this review we will first outline the basic features of the ordinary model and take a glimpse at a number of selective variations and modifications of the original model. Directed percolation process will be also discussed as a prototype of systems displaying a nonequilibrium phase transition. After a short review on SLE, we will provide an overview on existence of the scaling limit and conformal invariance of the critical percolation. We will also establish a connection with the magnetic models. Recent applications of the percolation theory in natural and artificial landscapes are also reviewed.

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Metadata

Authors
Saberi, A. A.
Venue
Physics Reports
Publisher
Elsevier BV
Published
2015-05
Volume
578
Pages
1-32
ISSN
0370-1573 (ISSN-L)
DOI
10.1016/j.physrep.2015.03.003
OpenAlex
W2041740704
Cited by
438
References
173
FWCI
58.71
Type
journal article
Language
en
Open access
green

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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.