MULTIFRACTAL PROPERTIES OF THE WAVE-FUNCTIONS OF THE SQUARE-LATTICE TIGHT-BINDING MODEL WITH NEXT-NEAREST-NEIGHBOR HOPPING IN A MAGNETIC-FIELD

We have used multifractal analysis for the wave functions to study the universality of the scaling properties of Harper's equation, the equa tion for a particle moving on a tight-binding square lattice in the pr esence of a gauge field, when coupling to next-nearest sites are added . We find that the properties of the wave functions are consistent wit h those of the spectra obtained by Han et al. [Phys. Rev. B 50, 11 365 (1994)]. The phase diagram consists of the three regions where the wa ve functions are localized, extended and critical, respectively.