MOBILITY EDGE AND LEVEL STATISTICS OF RANDOM TIGHT-BINDING HAMILTONIANS

The energy level spacing distribution of a tight-binding Hamiltonian i s monitored across the mobility edge for a fixed disorder strength. An y mixing of extended and localized levels is avoided in the configurat ional averages, thus approaching the critical point very closely and w ith high energy resolution. By finite-size scaling the method is shown to provide a very accurate estimate of the mobility edge and of the c ritical exponent for a cubic lattice with Lorentzian distributed diago nal disorder. Since no averaging in wide energy windows is required, t he method appears as a powerful tool for locating the mobility edges i n more complex models of real physical systems.