Probability Distribution of the Conductance at the Mobility Edge

The distribution of the conductance $P(g)$ at the critical point of the metal-insulator transition is presented for three- and four-dimensional orthogonal systems. The distribution is system-size independent but it depends on the dimension of the system. Its form is discussed and quantitative formulas for limiting cases g→0 and g→∞ are derived. The relation P(g)→0 in the limit g→0 is proven.