Localization in quasi-one-dimensional systems with a random magnetic field

We investigate the localization of electrons hopping on quasi-one-dimensional strips in the presence of a random magnetic field. In the weak-disorder region, by perturbative analytical techniques, we derive scaling laws for the localization length, xi, of the form xi proportional to 1/w(eta), where w is the size of magnetic disorder and the exponent eta assumes different values in the various energy ranges. Moreover, in the neighborhood of the energies where a new channel opens a certain rearrangement of the perturbation expansion leads to scaling functions for xi. Although the latter are in general quantitatively wrong, they correctly reproduce the corresponding eta exponents and the form of the scaling variables and are therefore useful for understanding the behavior of xi.