  The free energy at zero temperature of Coulomb gas systems in generic
dimension is considered as a function of a volume constraint. The transition
between the 'pulled' and the 'pushed' phases is characterised as a third-order
phase transition, in all dimensions and for a rather large class of isotropic
potentials. This suggests that the critical behaviour of the free energy at the
'pulled-to-pushed' transition may be universal, i.e., to some extent
independent of the dimension and the details of the pairwise interaction.
