Universal scaling, beta function, and metal-insulator transitions

We demonstrate a universal scaling form of longitudinal resistance in the quantum critical region of metal-insulator transitions. This is based on numerical results of three-dimensional Anderson transitions (with and without magnetic field), two-dimensional quantum Hall plateau to insulator transition, as well as experimental data of the recently discovered two-dimensional metal-insulator transition. The associated reflection symmetry and a peculiar logarithmic form of the beta function exist over a wide range in which the resistance can change by more than 1 order of magnitude. Interesting implications for the two-dimensional metal-insulator transition are discussed.