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Using analytical methods, we derive and extend previously obtained numericalresults on the low temperature properties of holographic duals tofour-dimensional gauge theories at finite density in a nonzero magnetic field.We find a new asymptotically AdS_5 solution representing the system at zerotemperature. This solution has vanishing entropy density, and the chargedensity in the bulk is carried entirely by fluxes. The dimensionless magneticfield to charge density ratio for these solutions is bounded from below, with aquantum critical point appearing at the lower bound. Using matched asymptoticexpansions, we extract the low temperature thermodynamics of the system. Abovethe critical magnetic field, the low temperature entropy density takes a simpleform, linear in the temperature, and with a specific heat coefficient divergingat the critical point. At the critical magnetic field, we derive the scalinglaw s ~ T^{1/3} inferred previously from numerical analysis. We also computethe full scaling function describing the region near the critical point, andidentify the dynamical critical exponent: z=3.  These solutions are expected to holographically represent boundary theoriesin which strongly interacting fermions are filling up a Fermi sea. They arefully top-down constructions in which both the bulk and boundary theories havewell known embeddings in string theory.

Magnetic Field Induced Quantum Criticality via new Asymptotically AdS_5 Solutions