Approximations of Mean Spherical Type for Lattice Percolation Models
STATE UNIV OF NEW YORK AT STONY BROOK DEPT OF CHEMISTRY
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We develop a general class of approximations of mean-spherical MSA type as a method for studying lattice percolation problems. We review the MSA and test certain extensions of it on lattice spin models. The relations between thermal spin models and percolation models. These extensions are used to treat both site and bond percolation models. In one low-density formulation of MSA, the threshold for bond percolation models. In one low density formulation of MSA, the threshold for bond percolation on a lattice is found to equal the value at the origin of the corresponding lattice Greens function. This result is extremely accurate for all lattices studied, and in all space dimensions d or 3. An accurate treatment is also given of the general site-bond problem. The entire percolation locus for this problem agrees very closely with the results of simulation. We also introduce a new method for studying percolation transitions which is a hybrid of the Kikuchi cluster approximation scheme and the MSA. The method is shown to give extremely good values for percolation thresholds while preserving the valuable features of the standards MSA. In particular, it provides a convenient means of computing the pair connectedness function. We also explore extensions of our approximations to treat directed site and bond percolation.
- Physical Chemistry