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We numerically investigate the effects of the random static magnetic field on a variety of electronic properties
(localization of electron wavefunctions, spectral correlations and electrical conductance) in substitutionally and topologically disordered alloys. For this, we generate two-dimensional substitutionally disordered alloys and simulate three-dimensional amorphous structures by a molecular dynamics algorithm. As Hamiltonian models, we use the usual Anderson tight-binding model for the  substitutional  disorder and  a  tight-binding model with a set of explicit s-type orbitals for the topological disorder.

We particularly focus on the effect of the random magnetic field on the localization of electron wavefunctions. In the presence of the substitutional disorder, we establish that the random magnetic field tends to delocalize the electron wavefunctions at the band center less than does the uniform magnetic field and it enhances the localization at the band edges. But, in the presence of the topological disorder, we observe the opposite effect. We show that the random magnetic field tends to delocalize the electron wavefunctions more than does the uniform magnetic field. In this respect, we demonstrate that the effect of the random magnetic field on the electron wavefunctions depends on the nature of the disorder.