Abstract
Several families of two-dimensional lattices are discussed for which the critical percolation density (pc) can be calculated exactly. The lattices are obtained by decorating lattices for which the value of the critical density for bond percolation is already known. It is shown that finite decorations of this type do not change the value of a critical exponent. By a sequence of decorations and lattice transformations the authors obtain a set of lattices of increasing coordination number q, and calculate the limit qpc for q to infinity for this family. The value of this limit is close to the numerical estimate of the corresponding critical density for continuum percolation.
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