We present a mean-field description of the zigzag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential $r^{-n}{e}^{-r/\lambda }$, that are confined by a power-law potential ($y^{\alpha }$). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of $\alpha$ and $n$. Close to the transition point for the zigzag phase transition, the scaling behavior of the order parameter is determined. For $\alpha =2$, the zigzag transition from a single to a double chain is of second order, while for $\alpha >2$, the one-chain configuration is always unstable and, for $\alpha <2$, the one-chain ordered state becomes unstable at a certain critical density, resulting in jumps of single particles out of the chain.

• Received 24 June 2011

DOI:https://doi.org/10.1103/PhysRevB.84.134106