A PRECISE DETERMINATION OF THE BACKBONE FRACTAL DIMENSION ON 2-DIMENSIONAL PERCOLATION CLUSTERS

The backbone fractal dimension d(f)B is Calculated on two-dimensional percolation dusters 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(f)B am 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 caws imply a value of d(f)B = 1.64 +/- 0.01 for the backbone fractal dimension. Because of the high degree of self-consistency of all the results, we believe that this estimate represents a considerably improved accuracy.