A precise determination of the backbone fractal dimension on two-dimensional percolation clusters

Abstract

The backbone fractal dimension d^B_f is calculated on two-dimensional percolation clusters at the percolation threshold. Studies are carried out on backbones defined in three different ways: bus bar, point-to-point, and with fully periodic boundaries. The estimates of d^B_f are obtained by measuring the variation of mass with radius for all clusters, and by means of finite size scaling on the bus bar backbones. All cases imply a value of d^B_f=1.64+or-0.01 for the backbone fractal dimension. Because of the high degree of self-consistency of all the results, the authors believe that this estimate represents a considerably improved accuracy.