Identical scaling behavior of dc and ac response near the percolation threshold in conductor-insulator mixtures

We measured dynamical dI/dV and ${\mathit{d}}^2$I/${\mathit{dV}}^2$ of carbon-wax mixtures near the percolation threshold as a function of dc voltage V. Scaled appropriately, dI/dV at small V fall on the same universal curve as one which also contains the real part of the frequency dependent conductance data. We find that at small q (scaled voltage or frequency), Σ(q)/Σ(0)-1 varies as ${\mathit{q}}^{\mathit{v}}$ where Σ is conductance and v is 1.36±0.06. An empirical form of the full scaling function that agrees well with known facts is proposed. We discuss how our results could be used to probe dangling clusters in the periphery of the conducting backbone, hitherto largely unexplored. Relevance to other systems like amorphous semiconductors is discussed.