Abstract
Using the conventional scaling approach as well as the renormalization group analysis in d = 2 + ε dimensions, we calculate the localization length ξ(B) in the presence of a magnetic field B. For the quasi-1D case the results are consistent with a universal increase of ξ(B) by a numerical factor when the magnetic field is in the range l ≪ lH ≲ ξ(0), l is the mean free path, lH is the magnetic length √ℏc/eB. However, for d ⩾ 2 where the magnetic field does cause delocalization there is no universal relation between ξ(B) and ξ(0). The effect of spin-orbit interaction is briefly considered as well.