Conductivity in the two-dimensional-site percolation problem

Measurements of the electrical conductivity of a 137 × 137-site simple-square screen mesh versus concentration of removed sites are reported. The new critical exponent is reported to be $t=1.38\mathrm{}\pm 0.12$ within an estimated critical region $\Delta x\sim 0.1$ about a critical percolation concentration $x_c=0.413\mathrm{}\pm 0.005$. A new effective medium theory, which includes overlap effects of adjacent removed sites, is derived, which gives $\frac{\sigma \mathrm{}\left(x\right)\mathrm{}}{\sigma \mathrm{}\left(0\right)\mathrm{}}=1-\pi x+\frac{\pi x^2}{2}$, in agreement with the experiment, except within the critical region.