  The absorbing-state transition in the three-dimensional contact process with
and without quenched randomness is investigated by means of Monte-Carlo
simulations. In the clean case, a reweighting technique is combined with a
careful extrapolation of the data to infinite time to determine with high
accuracy the critical behavior in the three-dimensional directed percolation
universality class. In the presence of quenched spatial disorder, our data
demonstrate that the absorbing-state transition is governed by an
unconventional infinite-randomness critical point featuring activated dynamical
scaling. The critical behavior of this transition does not depend on the
disorder strength, i.e., it is universal. Close to the disordered critical
point, the dynamics is characterized by the nonuniversal power laws typical of
a Griffiths phase. We compare our findings to the results of other numerical
methods, and we relate them to a general classification of phase transitions in
disordered systems based on the rare region dimensionality.
