Scaling up the Anderson transition in random-regular graphs

Abstract

We study the Anderson transition in lattices with the connectivity of a random-regular graph. Our results show that fractal dimensions are continuous across the transition, but a discontinuity occurs in their derivatives, implying the existence of a nonergodic metallic phase with multifractal eigenstates. The scaling analysis gives critical exponent = 0.94 0.08 and critical disorder W c = 18.17 0.02. Our data support that ergodicity is only recovered at zero disorder.

Topics & Concepts