Screening effects in Coulomb-frustrated phase separation

We solve a model of phase separation among two competing phases frustrated by the long-range Coulomb interaction in two and three dimensions, taking into account finite compressibility effects. In the limit of strong frustration in two dimension, we recover the results of Jamei [Phys. Rev. Lett. 94, 056805 (2005)] and the system always breaks into domains in a narrow range of densities, no matter how big is the frustration. For weak frustration in two dimension and for arbitrary frustration in three dimension, the finite compressibility of the phases is shown to play a fundamental role. Our results clarify the different roles of screening in two-dimensional and three-dimensional systems. We discuss the thermodynamic stability of the system near the transition of the phase-separated state and the possibility of observing it in real systems.