Hans Herrmann — Univ. Fed. do Ceara', PMMH, ESPCI, Paris, France #
Multiple Percolating Clusters #
Inspired by the formation of bigels, we developed a bond percolation model that yields multiple percolating clusters in three dimensions not only at the critical point, but also above it. Our simulations suggest that, in the thermodynamic limit, there is no upper limit to the number of percolating clusters. We show that in finite systems the maximum number of percolating clusters that can be obtained grows logarithmically with the lattice size. For equal initial densities in the thermodynamic limit, all clusters percolate at the same threshold and exhibit critical exponents consistent with the critical exponents of standard percolation. The threshold depends linearly on the initial density of species and the maximum and minimum initial densities decay exponentially with the maximal number of spanning clusters. We also study a percolation model in which we occupy bonds randomly and each time a spanning cluster appears we remove it. The maximum number n_max of spanning clusters one can harvest in this way grows with the system size like a power-law with exponent d-d_f. Also, the variance of n_max and the size distribution of the remaining finite clusters grow like power-laws.