# Correlated Percolation

**DOI:**https://doi.org/10.1007/978-3-642-27737-5_104-3

## Definition of the Subject

Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases, the theory predicts a geometrical transition at the percolation threshold, characterized in the percolative phase by the presence of a spanning cluster, which becomes infinite in the thermodynamic limit. Standard percolation usually deals with the problem when the constitutive elements of the clusters are randomly distributed. However, correlations cannot always be neglected. In this case, correlated percolation is the appropriate theory to study such systems. The origin of correlated percolation could be dated back to 1937 when Mayer (1937; Mayer and Ackermann 1937; Mayer and Harrison 1938; Mayer and Mayer 1940) proposed a theory to describe the condensation from a gas to a liquid in terms of mathematical clusters (for a review of cluster theory in simple fluids,...

## Keywords

Fractal Dimension Ising Model Critical Exponent Coexistence Curve Infinite Cluster## Bibliography

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