Numerical studies of localization in disordered systems

The results of numerical work on the Anderson model of disordered systems are presented. The sensitivity of the eigenvalues to the choice of periodic or antiperiodic boundary conditions is used as a criterion for localization, and the theory of this criterion is discussed. For the two dimensional square lattice this criterion gives a reasonably sharp result for the onset of localization which is not in conflict with other criteria of localization, and it is found that localization occurs far more easily than Anderson's theory suggests. For the diamond lattice the onset of localization is less sharply defined, and localization occurs less easily than for the square lattice, but more easily than in Anderson's theory.