Numerical test of the Percus–Yevick approximation for continuum media of adhesive sphere model at percolation threshold

We test accuracies of the Percus–Yevick (PY) approximation for percolation thresholds and long-range correlated probability functions for continuum media of the adhesive sphere model. We clarify the universality of the continuum percolation of such a model and estimate the percolation thresholds for selected values of the adhesiveness parameter τ. We then calculate the pair-connectedness function and the two-point cluster function at percolation point and compare them with the analytical predictions by the PY approximation. We find that the PY approximation yields the pecolation points overestimated for τ>0.161 and underestimated for τ<0.161. The analytical calculations of the probability functions exhibit fairly good agreement with the Monte Carlo data for τ=0.161. However, for other values of τ, the analytical results show marked deviations from the Monte Carlo data.