Abstract
The percolation properties of randomly centered rods and spheres are studied. The approach is based on the detailed study of frequencies of cluster occurrences. For random rods, the analytic expressions are derived for all cluster frequencies. It is then shown that one-dimensional systems of random rods exhibit critical behaviour withϱ c = ∞,γ = 1. For randomly centered spheres, we designed a numerical method for calculating the cluster frequencies. The approach is based on the principles of the Monte Carlo method. It can cope with clusters containing up to seven particles, which should suffice for the evaluation of accurate values of critical density and critical exponents.
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Borštnik, B., Lukman, D. Percolation of randomly centered rods and spheres. J Math Chem 8, 245–254 (1991). https://doi.org/10.1007/BF01166940
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DOI: https://doi.org/10.1007/BF01166940