  We show that strongly-coupled, translation-invariant holographic IR phases at
finite density can be classified according to the scaling behaviour of the
metric, the electric potential and the electric flux introducing four critical
exponents, independently of the details of the setup. Solutions fall into two
classes, depending on whether they break relativistic symmetry or not. The
critical exponents determine key properties of these phases, like thermodynamic
stability, the (ir)relevant deformations around them, the low-frequency scaling
of the optical conductivity and the nature of the spectrum for electric
perturbations. We also study the scaling behaviour of the electric flux through
bulk minimal surfaces using the Hartnoll-Radicevic order parameter, and
characterize the deviation from the Ryu-Takayanagi prescription in terms of the
critical exponents.
