Critical exponent and multifractality of states at the Anderson transition

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Abstract
Based on the assumptions of the existence of a one-paramter scaling law for a self-averaging scaling variable, and on a finite correlation length for the randomness, the lower bound for the critical exponent of the Anderson transition derived earlier by Chayes et al. [Phys. Rev. Lett. 57, 2999 (1986)] for uncorrelated disorder is generalized to the case of spatially correlated disorder. The bound is determined by the system-size dependence of the number of the random variables that are necessary to describe the transition. It is speculated how to relate the critical exponent to the multifractal properties of the states near the critical point. Exponents of several models are estimated and compared with numerical scaling calculations.