Two models of disorder in two dimensions are discussed. The first is a localization theory that treats noninteracting particles by perturbation theory in the weak scattering limit. A weak magnetic field is found to have strong effects on the previously predicted logarithmic rise in resistivity at low temperatures. No logarithmic divergence is found for the Hall constant. A second model treats the disorder scattering by conventional diagramatic technique but includes the effects of interactions. In a short communication it has previously been reported that the resistivity and Hall constant both show a logarithmic increase at low temperatures. The details of the calculation are reported here, together with an extension to thin wires which shows a $T^{-\frac{1}{2}}$ divergence in the resistivity.

• Received 16 April 1980

DOI:https://doi.org/10.1103/PhysRevB.22.5142