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 a change of the charge carrier density controlled by the 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 $d_c=3\mathrm{}$ 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.

• Received 31 December 2002

DOI:https://doi.org/10.1103/PhysRevB.67.092201