Diamagnetic susceptibility and current distributions in granular superconductors at percolation

We study a two-dimensional granular superconducting network at the percolation threshold under the influence of an external perpendicular magnetic field. By numerical simulations an the full nonlinear problem, we determine the scaling exponent for the magnetic susceptibility. Further, we report an the scaling properties of the current distribution. The scaling of the current is found to be independent of the value of the magnetic field. Our results are in contradiction with previous numerical results based on linearized equations. We find a value for the susceptibility exponent which does not agree with existing theoretical suggestions, but agrees perfectly with renormalization-group calculations.