MULTIFRACTALITY AND SCALING IN DISORDERED MESOSCOPIC SYSTEMS

We suggest a new method for investigating scaling properties of mesoscopic observables and their distributions in disordered systems showing metal-insulator transition. In such systems quantum interference effects lead to multifractal structure of eigenstates on scales much smaller than the correlation length of the transition which can be described by a set of exponents, the closed-integral-(alpha) spectrum. The analysis of closed-integral-(alpha) spectra can be extended to any scaling variable. Multifractality is an indication for broad distributions of these variables. If the transition is governed by one correlation length only then the closed-integral-(alpha) spectra of normalized scaling variables must be universal. The critical exponent v of the correlation length is determined by the value alpha-(0) where closed-integral-(alpha) takes its maximum and the scaling exponent of normalization x:nu-1 = alpha-(0) + x. As an illustrative example we calculate numerically the closed-integral-(alpha) spectra of eigenstates in the critical regime of 2 d disordered electron systems in high magnetic fields. We find similar closed-integral-(alpha) spectra indicating universal log-normal distributions of scaling variables.