  We discuss the effects of fluctuations of the local density of charged
dopants near a first order phase transition in electronic systems, that is
driven by change of charge carrier density controlled by doping level. Using a
generalization of the Imry-Ma argument, we find that the first order transition
is rounded by disorder at or below the lower critical dimension d_c=3, when at
least one of the two phases has no screening ability. The increase of d_c from
2 (as in the random field Ising model) to 3 is due to the long-range nature of
the Coulomb interaction. This result suggests that large clusters of both
phases will appear near such transitions due to disorder, in both two and three
dimensions. Possible implications of our results on manganites and underdoped
cuprates will be discussed.
