Abstract
Critical percolation density for temperature-dependent site percolation problem is calculated by using the lattice-gas model of atoms, especially inside the region where the sublattice ordering occurs (repulsive interaction) or liquid and gas phases coexist (attractive interaction). The square lattice is regarded as a resistor network. Any bond in the lattice is conductive or insulating whether both ends of the bond are occupied with atoms or not. The distribution of atoms is determined within the pair approximation from the lattice-gas Hamiltonian with nearest-neighbor interactions. Moreover a single-site effective-medium approximation which is similar to coherent potential approximation is used to obtain the critical percolation density.
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