Dielectric and diamagnetic susceptibilities near percolative superconductor-insulator transitions

Coarse-grained superconductor-insulator composites exhibit a superconductor-insulator transition governed by classical percolation, which should be describable by networks of inductors and capacitors. We study several classes of random inductor-capacitor networks on square lattices. We present a unifying framework for defining electric and magnetic response functions, and we extend the Frank-Lobb bond-propagation algorithm to compute these quantities by network reduction. We confirm that the superfluid stiffness scales approximately as [Formula: see text] as the superconducting bond fraction p approaches the percolation threshold p _c . We find that the diamagnetic susceptibility scales as [Formula: see text] below percolation, and as [Formula: see text] above percolation. For models lacking self-capacitances, the electric susceptibility scales as [Formula: see text]. Including a self-capacitance on each node changes the critical behavior to approximately [Formula: see text].