Annealed percolation: Determination of exponents in a correlated-percolation problem

Abstract

We describe a two-dimensional correlated-percolation model, which we call annealed percolation. In annealed percolation, attractive interactions between near-neighbor occupied sites produce a structure reminiscent of discontinuous metal films. We have carefully determined the percolation threshold ${\mathit{p}}_{\mathit{c}}$ and four exponents for this model: the correlation-length exponent \ensuremath{\nu}, the cluster-size-distribution exponent \ensuremath{\tau}, the fractal dimension of the infinite cluster ${\mathit{d}}_{\mathit{f}}$, and the electrical-conductivity exponent t. We find that all these exponents have the same values as in pure (uncorrelated) percolation. We also compute the electrical conductance G versus concentration p for this model and compare with the G vs p curves for pure-site and pure-bond percolation models.