Random fields at an absorbing state transition

We investigate a nonequilibrium phase transition in the presence of disorder that locally breaks the symmetry between two equivalent absorbing states. Such ``random-field'' disorder is known to have dramatic effects on equilibrium phase transitions; in low dimensions it can completely destroy the phase transition. In contrast, we demonstrate that the absorbing state transition of the one-dimensional generalized contact process persists in the presence of random fields. However, the dynamics in the inactive phase becomes ultraslow. We illustrate our theory by means of large-scale Monte-Carlo simulations.