Recent experiments show that charge-density wave correlations are prevalent in underdoped
cuprate superconductors. The correlations are short-ranged at weak magnetic fields but their in-
tensity and spatial extent increase rapidly at low temperatures beyond a crossover field. Here we
consider the possibility of long-range charge-density wave order in a model of a layered system where
such order competes with superconductivity. We show that in the clean limit, low-temperature long-
range order is stabilized by arbitrarily weak magnetic fields. This apparent discrepancy with the
experiments is resolved by the presence of disorder. Like the field, disorder nucleates halos of charge-
density wave, but unlike the former it also disrupts inter-halo coherence, leading to a correlation
length that is always finite. Our results are compatible with various experimental trends, including
the onset of longer range correlations induced by inter-layer coupling above a characteristic field
scale