Strict parabolicity of the multifractal spectrum at the Anderson transition

Abstract

Using the well-known "algebra of multifractality", we derive the functional equation for anomalous dimensions Δ_q, whose solution Δ_q=aq(q-1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of σ-models with the initial disordered systems is not exact.

6 pages, 3 figures included