Invasion percolation between two sites in two, three, and four dimensions

The mass distribution of invaded clusters in non-trapping invasion percolation between an injection site and an extraction site has been studied, in two, three, and four dimensions. This study is an extension of the recent study focused on two dimensions by Araújo et al. A.D. Araújo, T.F. Vasconcelos, A.A. Moreira, L.S. Lucena, J.S. Andrade Jr., Phys. Rev. E 72 (2005) 041404] with respect to higher dimensions. The mass distribution exhibits a power-law behavior, P(m)∝m^−α. It has been found that the index α for p_e<p_c, p_c being the percolation threshold of a regular percolation, appears to be independent of the value of p_e and is also independent of the lattice dimensionality. When p_e=p_c, α appears to depend marginally on the lattice dimensionality, and the relation α=τ−1, τ being the exponent associated with cluster size distribution of a regular percolation via n_s∝s^−τ, appears to be valid.