The statistics of critical wave functions at the Anderson transition in three and four dimensions are studied numerically. The distribution of the inverse participation ratios (IPRs) $P_q$ is shown to acquire a scale-invariant form in the limit of large system size. Multifractality spectra governing the scaling of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR statistics and the multifractality at the Anderson transition in a high spatial dimensionality are formulated.

• Received 3 May 2002

DOI:https://doi.org/10.1103/PhysRevB.66.033109