  Using exact diagonalization technique, we investigate the many-body
localization phenomenon in the 1D Heisenberg chain comparing several disorder
models. In particular we consider a family of discrete distributions of
disorder strengths and compare the results with the standard uniform
distribution. Both statistical properties of energy levels and the long time
non-ergodic behavior are discussed. The results for different discrete
distributions are essentially identical to those obtained for the continuous
distribution, provided the disorder strength is rescaled by the standard
deviation of the random distribution. Only for the binary distribution
significant deviations are observed.
