Universal multifractal behaviour for phonons and electrons at the Anderson transition

摘要

We compare the properties of the multifractal singularity spectrum for both electron and phonon Anderson localization-delocalization transitions. The singularity spectrum for phonons is numerically obtained for continuous mass or spring constant disorder with distribution widths Δm = 1.2 and Δk = 10 at critical frequencies ω_c~2 = 12.681k/m and ω_c~2 = 19.75k/m, respectively. The spectra are compared to the numerically obtained electronic potential disordered metalinsulator transition at energy E = 0. We see that the spectra are in good agreement and as in all cases the critical exponents characterising the transitions are the same within error, and conclude that these models exhibit the same critical properties and are of the same orthogonal universality class.