Bubble, stripe, and ring phases in a two-dimensional cluster with competing interactions

A system of classical charged particles confined in a two-dimensional trap and interacting through a competing short-range attraction and long-range repulsion potential is studied. The structure of the system strongly depends on the interaction range of the short-range attraction potential and the total number of particles. Depending on the appropriate choice of parameters for the attractive potential, the particles organize themselves in bubbles, stripe phases, and ringlike configurations, or combinations of both of them. Detailed phase diagrams are presented for systems consisting of N=2 up to N=6 particles. General rules are derived for the different subsequent transitions between those configurations and how the ground state configuration of a large system can be deduced from the one of a small number of particles.