Universal substructures of percolation clusters: The skeleton

The authors define the 'skeleton' of a cluster aggregate as the set of all sites belonging to the shortest paths connecting a chosen site with the Lth chemical shell surrounding that site. The fractal properties of skeletons of percolation clusters at criticality have been studied, and it is inferred that the mass of the skeleton M_s scales with the chemical distance l (for l<<L) as M_s approximately (l_l^s), where (d_l^s)=1 is universal for l<or=d<or=6. Numerical evidence which supports this conclusion is presented for d=2, and an analytical proof is given for d=6.