  The appearance of the light Higgs boson at the LHC is difficult to explain,
particularly in light of naturalness arguments in quantum field theory. However
light scalars can appear in condensed matter systems when parameters (like the
amount of doping) are tuned to a critical point. At zero temperature these
quantum critical points are directly analogous to the finely tuned standard
model. In this paper we explore a class of models with a Higgs near a quantum
critical point that exhibits non-mean-field behavior. We discuss the
parametrization of the effects of a Higgs emerging from such a critical point
in terms of form factors, and present two simple realistic scenarios based on
either generalized free fields or a 5D dual in AdS space. For both of these
models we consider the processes $gg\to ZZ$ and $gg\to hh$, which can be used
to gain information about the Higgs scaling dimension and IR transition scale
from the experimental data.
