Magnetoresistance of two-dimensional tight-binding electrons in a weak magnetic field

We study the Anderson model on a two-dimensional square lattice with an applied weak magnetic field B which causes the hopping matrix elements to have Peierls phase factors. The recursion method is applied and B dependent conductivity σ(B) is calculated from the Kubo formula for different system sizes N and degree of disorder W. For large W there is no appreciable change of σ(B) with B, but its system size dependence is first an increasing and then a decreasing behavior.