  Quantum critical points exist at zero temperature, yet, experimentally their
influence seems to extend over a large part of the phase diagram of systems
such as heavy-fermion compounds and high-temperature superconductors.
Theoretically, however, it is generally not known over what range of parameters
the physics is governed by the quantum critical point. We answer this question
for the spin-density wave to fermi-liquid quantum critical point in the
two-dimensional Hubbard model. This problem is in the $d=2,z=2$ universality
class. We use the Two-Particle Self-Consistent approach, which is accurate from
weak to intermediate coupling, and whose critical behavior is the same as for
the self-consistent-renormalized approach of Moriya. Despite the presence of
logarithmic corrections, numerical results demonstrate that quantum critical
scaling for the static magnetic susceptibility can extend up to very high
temperatures but that the commensurate to incommensurate crossover leads to
deviations to scaling.
