Critical dimensionality in the Anderson-Mott transition

An argument by Edwards et al. (1977) regarding four as the critical dimension in the Anderson-Mott transition is reviewed. It is pointed out that convergence of the Green's function series for some random systems is not determined by its expectation value alone. A simple model also demands convergence of the series for the variances and this series, which is identical to that for the two-particle Green's function for this model, has eight as the critical dimension.