  The structural transitions of the ground state of a system of repulsively
interacting particles confined in a quasi-one-dimensional channel, and the
effect of the interparticle interaction as well as the functional form of the
confinement potential on those transitions are investigated. Although the
non-sequential ordering of transitions (non-SOT), i.e.
$1$-$2$-$4$-$3$-$4$-$5$-$6$-$...$ sequence of chain configurations with
increasing density, is widely robust as predicted in a number of theoretical
studies, the sequential ordering of transitions (SOT),
i.e.~$1$-$2$-$3$-$4$-$5$-$6$-$...$ chain, is found as the ground state for
long-ranged interparticle interaction and hard-wall-like confinement
potentials. We found an energy barrier between every two different phases
around its transition point, which plays an important role in the preference of
the system to follow either a SOT or a non-SOT. However, that preferential
transition requires also the stability of the phases during the transition.
Additionally, we analyze the effect of a small structural disorder on the
transition between the two phases around its transition point. Our results show
that a small deformation of the triangular structure, change dramatically the
picture of the transition between two phases, removing in a considerable region
the non-SOT in the system. This feature could explain the fact that the non-SOT
is, up to now, not observed in experimental systems, and suggests a more
advanced experimental set-up to detect the non-SOT.
