Recent advances in percolation theory and its applications
By Abbas Ali Saberi. 2015
410 citations recorded by the source corpus.
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.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bdd49766fede5fd62810d43ccaff1390b7fa0908
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In Condensed Matter Physics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Anomalous critical and supercritical phenomena in explosive percolation (2015, background): “ld not be included in this brief review which is focused on the novel properties and classes of EP phenomena. For recent reviews of advances and challenges in the general field of percolation see Ref. [85, 86]. See Ref. [27] for a comprehensive review of models displaying EP. Acknowledgements: We tha”