  A chain of singly-charged particles, confined by a harmonic potential,
exhibits a sudden transition to a zigzag configuration when the radial
potential reaches a critical value, depending on the particle number. This
structural change is a phase transition of second order, whose order parameter
is the crystal displacement from the chain axis. We study analytically the
transition using Landau theory and find full agreement with numerical
predictions by [J. Schiffer Phys. Rev. Lett. 70, 818 (1993)] and [Piacente et
al Phys. Rev. B 69, 045324 (2004)]. Our theory allows us to determine
analytically the system's behaviour at the transition point.
