We find that when two or more spanning clusters exist at the percolation threshold, the mass of each scales with the same fractal dimension D = 1.89 in two dimensions and D = 2.53 in three dimensions. We also determine the ratios of the masses of the spanning clusters. In two dimensions, this is done for different lattices of different shapes. In the case of two spanning clusters, the ratio of the larger spanning cluster to the smaller lies around 1.4 for two dimensions, almost independent of lattice structure and shape.
- Fractal Dimension
- Spanning Probabilities