Critical exponents of dynamical conductivity in 2D percolative superconductor-insulator transitions: three...

We simulate three types of random inductor-capacitor (LC) networks on [Formula: see text] square lattices. We calculate the dynamical conductivity using an equation-of-motion method in which timestep error is eliminated and windowing error is minimized. We extract the critical exponent a such that [Formula: see text] at low frequencies. The results suggest that there are three different universality classes. The [Formula: see text] model, with capacitances from each site to ground, has a  =  0.314(4). The [Formula: see text] model, with capacitances along bonds, has a  =  0. The [Formula: see text] model, with both types of capacitances, has a  =  0.304(1). This implies that classical percolative 2D superconductor-insulator transitions (SITs) generically have [Formula: see text] as [Formula: see text]. Therefore, any experiments that give a constant conductivity as [Formula: see text] must be explained in terms of quantum effects.