We investigate the diffusion and conductance behavior of binary Archimedean lattices and binary layer systems (with bonds of conductances G A and G B between the sites) close to the percolation threshold (of the G A -lattice) by numerical simulations and by scaling theories. We are interested in possible influence factors of geometry, defects and thickness on the conductivity and in particular on the critical exponents of the phase transition between insulating and conducting phases. We aim for information that will help to decide if experimentally observed transitions between good and poor conductors are due to percolation effects, even if in real experiments, the pure theoretically expected behavior is often not exactly reproduced. We find that Archimedean lattices of all kinds show the expected universal behavior in high precision. Layer systems show a crossover from 2D to 3D behavior that becomes visible beyond a certain layer thickness. We discuss by which processes the universal behavior might be disturbed.
