  We consider a $d$-dimensional gas in canonical equilibrium under pairwise
screened Coulomb repulsion and external confinement, and subject to a volume
constraint. We show that its excess free energy displays a generic third-order
singularity separating the pushed and pulled phases, irrespective of range of
the pairwise interaction, dimension and details of the confining potential. The
explicit expression of the excess free energy is universal and interpolates
between the Coulomb (long-range) and the delta (zero-range) interaction. The
order parameter of this transition - the electrostatic pressure generated by
the surface excess charge - is determined by invoking a fundamental energy
conservation argument.
