  We investigate the infrared behavior of the spectrum of scalar-dressed,
asymptotically Anti de Sitter (AdS) black brane (BB) solutions of effective
holographic models. These solutions describe scalar condensates in the dual
field theories. We show that for zero charge density the ground state of these
BBs must be degenerate with the AdS vacuum, must satisfy conformal boundary
conditions for the scalar field and it is isolated from the continuous part of
the spectrum. When a finite charge density is switched on, the ground state is
not anymore isolated and the degeneracy is removed. Depending on the coupling
functions, the new ground state may possibly be energetically preferred with
respect to the extremal Reissner-Nordstrom AdS BB. We derive several properties
of BBs near extremality and at finite temperature. As a check and illustration
of our results we derive and discuss several analytic and numerical, BB
solutions of Einstein-scalar-Maxwell AdS gravity with different coupling
functions and different potentials. We also discuss how our results can be used
for understanding holographic quantum critical points, in particular their
stability and the associated quantum phase transitions leading to
superconductivity or hyperscaling violation.
