Numerical estimates of the Hausdorff dimension of the largest cluster and its backbone in the percolation problem in two dimensions

We present numerical estimates of the Hausdorff dimension D of the largest cluster and its "backbone" in the percolation problem on a square lattice as a function of the concentration p. We fine that D is an approximately linear function of p in the region near p=pc (0.59) with a dimension about equal to that of a self-avoiding walk when p=0.455. The dimension of the backbone, or biconnected part, of the largest cluster equals that of the self-avoiding walk when ppc. At p=pc the dimension of the largest cluster equals the anomalous dimension introduced by Stanley et al.