  We study the relationship between charge density ({\rho}) and chemical
potential ({\mu}) for an array of Lorentz invariant 3 + 1 dimensional
holographic field theories with the minimal structure of a conserved charge.
The systems considered include Dp-Dq probe brane constructions and probe and
backreacted 'bottom-up' models with gauge and scalar fields. In all cases, at
large density, the relationship is well modelled by a power law behaviour of
the form {\rho} $\propto$ {\mu}^{\alpha}. A variety of powers {\alpha} are
found in the brane systems while in most of the bottom-up models {\alpha} is
determined by the underlying conformal symmetry. Further, it is demonstrated
that basic thermodynamical and causality constraints demand {\alpha} \geq 1, a
condition that was realized in each system considered.
