Crystals consisting of ions may be formed as a result of the application of a confining potential. Phase transitions in such crystals result from the competition between the confining potential and the repulsion between the ions. In one dimension, at zero temperature, at such a transition a zigzag forms. The quantum effects are described by the Ising model in a transverse field. Two-dimensional structures undergo a buckling instability described by a rich phase diagram. The system is modeled by the six state clock model, exhibiting a Kosterlitz-Thouless transition and quasi-long-range order at finite temperatures as well as a transition to quantum long-range order. The models to be presented provide an idealized description for experiments on cold atoms. In the seminar joint work in collaboration with Daniel Podolsky, Efrat Shishoni and Giovanna Morigi will be reported.