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Percolation and variable-range hopping in random systems with spherical site symmetry

Authors
Journal
Solid State Communications
0038-1098
Publisher
Elsevier
Publication Date
Volume
17
Issue
7
Identifiers
DOI: 10.1016/0038-1098(75)90713-9

Abstract

Abstract We show that the numerical work of Seager and Pike 1,2 suggests that the critical volume fraction (CVF) is a constant for sites of spherical symmetry in n dimensions, with CVF⋍nπ 1−n for small n. The average number of bonds per site, B ̄ c , is calculated for a random distribution of site radii, and shown to agree with the Monte Carlo calculation. Analysis of a model having spherical site symmetry in (position-energy) space yields percolation constants C 2 = 2.1, C 3 = 2.6. This calculation indicates that there is an anomaly in some estimated values for the AHL percolation model. The physical significance of our model and its possible use in hard-core problems is discussed.

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