Metal-insulator transition in the four-dimensional Anderson model

The metal-insulator transition in the four-dimensional Anderson model is studied numerically using the finite-size-scaling method. Critical disorder is found and the spectrum of Lyapunov exponents of the transfer matrix is shown to change from linear to the third-root shape when the system undergoes the metal-insulator transition. On the basis of our results, we conjecture the dimension dependence of the critical disorder and of the spectrum of Lyapunov exponents for dimension d>2.