Universal Aspects of Coulomb Frustrated Phase Separation

We study the consequences of Coulomb interactions on a system undergoing a putative first order phase transition. In two dimensions (2D), near the critical density, the system is universally unstable to the formation of new intermediate phases, which we call ``electronic microemulsion phases,'' which consist of an intermediate scale mixture of regions of the two competing phases. A corollary is that there can be no direct transition as a function of density from a 2D Wigner crystal to a uniform electron liquid. In 3D, if the strength of the Coulomb interactions exceeds a critical value, no phase separation occurs, while for weaker Coulomb strength, electronic microemulsions are inevitable. This tendency is considerably more pronounced in anisotropic (quasi 2D or quasi 1D) systems, where a devil's staircase of transitions is possible.