  We study the relativistic O(N) field theory near the quantum critical point
in 2+1 dimensions for N=2 and N=3. The scalar susceptibility is evaluated by
Monte Carlo simulation. We show that the spectrum contains a peak associated
with the Higgs mode, which remains well-defined all the way to the critical
point. The fidelity of this peak and the amplitude ratio between the critical
energy scales on both sides of the transition are computed.
