title: Multifractal analysis with the probability density function at the three-dimensional anderson transition.
abstract: The probability density function (PDF) for critical wave function amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size corrections is properly analyzed. We show the non-Gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and the possible existence of termination points. A PDF-based multifractal analysis is shown to be a valid alternative to the standard approach based on the scaling of inverse participation ratios.
authors.affiliation: Department of Physics and Centre for Scientific Computing, University of Warwick, Coventry, CV4 7AL, United Kingdom. A.Rodriguez-Gonzalez@warwick.ac.uk
authors.forename: Alberto
authors.initials: A
authors.lastname: Rodriguez
authors.forename: Louella J
authors.initials: LJ
authors.lastname: Vasquez
authors.forename: Rudolf A
authors.initials: RA
authors.lastname: Römer