  Second order phase transitions are universally driven by an order parameter
which becomes trivial at the critical point. At the same time, collective
excitations which involve the amplitude of the order parameter develop a gap
which smoothly closes to zero at criticality. We develop analytical techniques
to study this "Higgs" mode in holographic systems which undergo a continuous
phase transition at finite temperature and chemical potential. This allows us
to study the linear response of the system at energy scales of the order of the
gap. We express the Green's functions of scalar operators in terms of
thermodynamic quantities and a single transport coefficient which we fix in
terms of black hole horizon data.
