  We investigate the nonequilibrium phase transition in the disordered contact
process in the presence of long-range spatial disorder correlations. These
correlations greatly increase the probability for finding rare regions that are
locally in the active phase while the bulk system is still in the inactive
phase. Specifically, if the correlations decay as a power of the distance, the
rare region probability is a stretched exponential of the rare region size
rather than a simple exponential as is the case for uncorrelated disorder. As a
result, the Griffiths singularities are enhanced and take a non-power-law form.
The critical point itself is of infinite-randomness type but with critical
exponent values that differ from the uncorrelated case. We report large-scale
Monte-Carlo simulations that verify and illustrate our theory. We also discuss
generalizations to higher dimensions and applications to other systems such as
the random transverse-field Ising model, itinerant magnets and the
superconductor-metal transition.
