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 = χq(q–1) corresponds to strict parabolicity of the multifractal spectrum. This result demonstrates clearly that a correspondence of the nonlinear σ-models with the initial disordered systems is not exact.