  We report on numerically exact determinantal quantum Monte Carlo simulations
of the onset of spin-density wave (SDW) order in itinerant electron systems
captured by a sign-problem-free two-dimensional lattice model. Extensive
measurements of the SDW correlations in the vicinity of the phase transition
reveal that the critical dynamics of the bosonic order parameter are well
described by a dynamical critical exponent z = 2, consistent with Hertz-Millis
theory, but are found to follow a finite-temperature dependence that does not
fit the predicted behavior of the same theory. The presence of critical SDW
fluctuations is found to have a strong impact on the fermionic quasiparticles,
giving rise to a dome-shaped superconducting phase near the quantum critical
point. In the superconducting state we find a gap function that has an opposite
sign between the two bands of the model and is nearly constant along the Fermi
surface of each band. Above the superconducting $T_c$ our numerical simulations
reveal a nearly temperature and frequency independent self energy causing a
strong suppression of the low-energy quasiparticle spectral weight in the
vicinity of the hot spots on the Fermi surface. This indicates a clear
breakdown of Fermi liquid theory around these points.
