Phase separation frustrated by the long-range Coulomb interaction. II. Applications

Abstract

The theory of first-order density-driven phase transitions with frustration due to the long-range Coulomb (LRC) interaction developed in paper I of this series is applied to the following physical systems: (i) the low-density electron gas, (ii) electronic phase separation in the low-density three-dimensional $t\ensuremath{-}J$ model, and (iii) in the manganites near the charge-ordered phase. We work in the approximation that the density within each phase is uniform and we assume that the system separates into spherical drops of one phase hosted by the other phase with the distance between drops and the drop radius much larger than the interparticle distance. For (i) we study a well-known apparent instability related to a negative compressibility at low densities. We show that this does not lead to macroscopic drop formation as one could expect naively and the system is stable from this point of view. For (ii) we find that the LRC interaction significantly modifies the phase diagram favoring uniform phases and mixed states of antiferromagnetic (AF) regions surrounded by metallic regions over AF regions surrounded by empty space. For (iii) we show that the dependence of local densities of the phases on the overall density found in paper I gives a nonmonotonous behavior of the Curie temperature on doping in agreement with experiments.