Universal Intermediate Phases of Dilute Electronic and Molecular Glasses

Generic intermediate phases with anomalous properties exist over narrow composition ranges adjacent to connectivity transitions. Analysis of both simple classical and complex quantum percolation shows how topological concepts can be used to understand many mysterious properties of high temperature superconductors, including the remarkably similar phase diagrams of ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ and ${\mathrm{C}}_{60}^{+y}$. Predictions are made for novel threshold behavior of the impurity band metal-insulator transition in two dimensions.