Percolation and cluster structure parameters: The radius of gyration

The squared radius of gyration of percolation clusters are determined in terms of the clusters' second spatial moments using the enhanced Hoshen - Kopelman algorithm for square and triangular lattices containing sites. Correlation length exponents and related exponents as well as their corresponding amplitudes are calculated in terms of the squared radius of gyration above and below the percolation threshold. A coefficient for cluster compactness that is based on the squared radius of gyration of a cluster is introduced. That coefficient is compared with a similar coefficient of compactness that is based on the cluster cyclomatic number.

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