  We construct a class of quantum critical points with non-mean-field critical
exponents via holography. Our approach is phenomenological. Beginning with the
D3/D5 system at nonzero density and magnetic field which has a chiral phase
transition, we simulate the addition of a third control parameter. We then
identify a line of quantum critical points in the phase diagram of this theory,
provided that the simulated control parameter has dimension less than two. This
line smoothly interpolates between a second-order transition with mean-field
exponents at zero magnetic field to a holographic
Berezinskii-Kosterlitz-Thouless transition at larger magnetic fields. The
critical exponents of these transitions only depend upon the parameters of an
emergent infrared theory. Moreover, the non-mean-field scaling is destroyed at
any nonzero temperature. We discuss how generic these transitions are.
