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We consider a $d$-dimensional gas in canonical equilibrium under pairwisescreened Coulomb repulsion and external confinement, and subject to a volumeconstraint. We show that its excess free energy displays a generic third-ordersingularity separating the pushed and pulled phases, irrespective of range ofthe pairwise interaction, dimension and details of the confining potential. Theexplicit expression of the excess free energy is universal and interpolatesbetween the Coulomb (long-range) and the delta (zero-range) interaction. Theorder parameter of this transition - the electrostatic pressure generated bythe surface excess charge - is determined by invoking a fundamental energyconservation argument.

Universality of the weak pushed-to-pulled transition in systems with repulsive interactions