In search for phase transitions in Casimir force between percolating metal lattices

We provide a derivation of the percolation threshold for a two-dimensional triangular lattice. We then proceed to model an ensemble of skewed square lattices with randomly punched out squares, which is topologically equivalent to triangular lattice percolation. We investigate the behavior of the magnitude of the Casimir force between the percolating plate and the solid plate. We find evidence which suggests that connectivity of the percolating plate has an effect on the long wavelength current excitations on the surface of the conductors and consequently on the magnitude of the Casimir force.