  We study a one dimensional Coulomb system, where two charged colloids are
neutralized by a collection of point counterions, with global neutrality.
Temperature being given, two situations are addressed: the colloids are either
kept at fixed positions (canonical ensemble), or the force acting on the
colloids is fixed (isobaric-isothermal ensemble). The corresponding partition
functions are worked out exactly, in view of determining which arrangement of
counterions is optimal: how many counterions should be in the confined segment
between the colloids? For the remaining ions outside, is there a left/right
symmetry breakdown? We evidence a cascade of transitions, as system size is
varied in the canonical treatment, or as pressure is increased in the isobaric
formulation.
