Statistics of Red Sites on Elastic and Full Backbone

Abstract

We investigate the number of red sites on the elastic and real backbone when right at the percolation threshold a spanning cluster exists between two sites at opposite faces of the lattice and found that it scales in the same way as in the case of percolation between two plates. We also find out that the number of common red sites scales similarly for both kinds of backbones for percolation between pairs of sites on opposite faces of the lattice. Our statistics for several quantities show that the the exponent for the elastic backbone approaches the one of the full backbone as dimensionality is increased.