# Localization in quasi-one-dimensional systems with a random magnetic field. Academic Article

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### abstract

• 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, \ensuremath{\xi}, of the form \ensuremath{\xi}\ensuremath{\propto}1/${\mathit{w}}^{\mathrm{\ensuremath{\eta}}}$, where w is the size of magnetic disorder and the exponent \ensuremath{\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 \ensuremath{\xi}. Although the latter are in general quantitatively wrong, they correctly reproduce the corresponding \ensuremath{\eta} exponents and the form of the scaling variables and are therefore useful for understanding the behavior of \ensuremath{\xi}. \textcopyright{} 1996 The American Physical Society.

### publication date

• January 1, 1996