Scaling Equations from a Self-Consistent Theory of Anderson Localization

The conductance of a disordered system of finite volume Lᵈ (d spatial dimensions) is calculated by making use of a recently developed self-consistent theory. Scaling equations are derived for the dimensionless conductance g and the scaling function β(g(L))=dlng/dlnL is explicitly calculated for arbitrary dimension d. It is shown that the theory obeys scaling in the sense of Wegner, Thouless, and Abrahams et al.