Mean valence of sites in non-percolating clusters

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Abstract
The authors present Monte Carlo and series results for the mean valence ( nu )F of non-percolating clusters on the square lattice and corresponding series results for the simple cubic lattice. Mimic functions have been constructed from the series which, for the square lattice, agree well with the Monte Carlo data, for a wide range of densities. They have shown that if the percolation probability is continuous at rho c then ( nu )F is continuous at rho c, and have presented a heuristic argument which indicates that ( nu )1, the mean valence of a site in a percolating cluster, is greater than ( nu )F, at rho c. This allows one to infer the asymptotic behaviour of ( nu )F in the region of rho c.

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