A PRECISE CHARACTERIZATION OF 3-DIMENSIONAL PERCOLATING BACKBONES

The backbones of three-dimensional critical percolation clusters are e xtracted and the fractal dimension is accurately calculated using vari ous mass-scaling and box-counting techniques to be d(f)B = 1.855 +/- 0 .015. The eigenvalue spectrum of the Brownian transition probability m atrix is studied numerically, which results in the estimates d(w)B = 3 .13 +/- 0.03 for the walk dimension and d(s)B = 1.18 +/- 0.01 for the spectral dimension of the backbone. Independent calculation of all thr ee quantities allows the conductivity exponent mu to be determined and also allows the validity of the scaling relation d(s) = 2d(f)/d(w) pr oposed by Alexander and Orbach to be tested on the backbone.