A NEW SCHEME TO PERCOLATION THRESHOLDS

Using a ferromagnetic Ising model, a new lattice homogeneity breaking approach (HBA) for two-dimensional site dilution is presented. The critical temperature is stated to result from an energetic balance between the cluster center and its surface. This definition produces a breaking in the homogeneity of the system between the fluctuating cluster magnetization and the mean bulk counterpart. Site dilution is then found to generate additional breaking of the system homogeneity, with the introduction of a generalized surface effect which makes our procedure qualitatively different from the Bethe one. The HBA results in a simple new analytic expression for site percolation thresholds, which reproduces the exact values or numerical estimates for all lattice topologies in dimension two, within few percent.