In ion chains a second order phase transition between chain and zigzag phases takes place as the density of ions or the transverse confining potential is varied. A simplified model is introduced and analyzed in the framework of mean field theory, relevant for zero temperature. In presence of quantum fluctuations the system is described by Ising model in a transverse field that is in the universality class of the 2D classical Ising model. The cross-over from the classical to quantum critical behavior was calculated. The experimental realizations will be discussed.