Probability Distribution of the Conductance at the Mobility Edge

The distribution of the conductance $P\left(g\right)$ 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 $g\to 0$ and $g\to \infty$ are derived. The relation $P\left(g\right)\to 0$ in the limit $g\to 0$ is proven.