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We investigate the infrared behavior of the spectrum of scalar-dressed,asymptotically Anti de Sitter (AdS) black brane (BB) solutions of effectiveholographic models. These solutions describe scalar condensates in the dualfield theories. We show that for zero charge density the ground state of theseBBs must be degenerate with the AdS vacuum, must satisfy conformal boundaryconditions for the scalar field and it is isolated from the continuous part ofthe spectrum. When a finite charge density is switched on, the ground state isnot anymore isolated and the degeneracy is removed. Depending on the couplingfunctions, the new ground state may possibly be energetically preferred withrespect to the extremal Reissner-Nordstrom AdS BB. We derive several propertiesof BBs near extremality and at finite temperature. As a check and illustrationof our results we derive and discuss several analytic and numerical, BBsolutions of Einstein-scalar-Maxwell AdS gravity with different couplingfunctions and different potentials. We also discuss how our results can be usedfor understanding holographic quantum critical points, in particular theirstability and the associated quantum phase transitions leading tosuperconductivity or hyperscaling violation.

Infrared Behavior of Scalar Condensates in Effective Holographic Theories