  Many correlated materials display a quantum critical point between a
paramagnetic and a SDW state. The SDW wave vector connects points (hot spots)
on opposite sides of the Fermi surface. The Fermi velocities at these pairs of
points are in general not parallel. Here we consider the case where pairs of
hot spots coalesce, and the wave vector (\pi,\pi) of the SDW connects hot spots
with parallel Fermi velocities. Using the specific example of electron-doped
cuprates, we first show that Kanamori screening and generic features of the
Lindhard function make this case experimentally relevant. The temperature
dependence of the correlation length, the spin susceptibility and the
self-energy at the hot spots are found using the Two-Particle-Self-Consistent
theory and specific numerical examples worked out for parameters characteristic
of the electron-doped cuprates. While the curvature of the Fermi surface at the
hot spots leads to deviations from perfect nesting, the pseudo-nesting
conditions lead to drastic modifications to the temperature dependence of these
physical observables: Neglecting logarithmic corrections, the correlation
length \xi scales like 1/T, i.e. z=1 instead of the naive z=2, the (\pi,\pi)
static spin susceptibility \chi like $1/\sqrt T$, and the imaginary part of the
self-energy at the hot spots like $T^{3/2}$. The correction $T_1^{-1}\sim
T^{3/2}$ to the Korringa NMR relaxation rate is subdominant. We also consider
this problem at zero temperature, or for frequencies larger than temperature,
using a field-theoretical model of gapless SDW fluctuations interacting with
fermions. The imaginary part of the fermionic self-energy close to the hot
spots scales as $-\omega^{3/2}\log\omega$. This is less singular than earlier
predictions of the form $-\omega\log\omega$. The difference arises from the
effects of umklapp terms that were not included in previous studies.
