Superconducting diamagnetism near the percolation threshold: numerical study

The authors investigate numerically the magnetic properties of a random superconducting network, which models random superconductor-insulator mixtures. Bonds between nearest-neighbour sites on a square lattice are chosen to be independently superconducting with probability p, and insulating with probability 1-p. A new numerical method is used to investigate loop statistics in these percolating networks. The diamagnetic susceptibility chi as a function of the superconducting fraction p is calculated. Close to the percolation threshold p c , chi shows a singular behaviour as a function of (p c -p). The numerical results exhibit a finite-size scaling which enables one to deduce the critical exponent of chi from calculations on relatively small samples. The numerical results are in good agreement with the predictions of recent scaling theory and differ from those made by previous workers.