  We perform an instability analysis of the Emery three-band model at hole
doping and weak coupling within a channel-decomposed functional renormalization
group flow proposed in Phys. Rev. B 79, 195125 (2009). In our approach,
momentum dependences are taken into account with improved precision compared to
previous studies of related models. Around a generic parameter set, we find a
strong competition of antiferromagnetic and d-wave Cooper instabilities with a
smooth behavior under a variation of doping and additional hopping parameters.
For increasingly incommensurate ordering tendencies in the magnetic channel,
the d-wave pairing gap is deformed at its maxima. Comparing our results for the
Emery model to those obtained for the two-dimensional one-band Hubbard model
with effective parameters, we find that, despite considerable qualitative
agreement, multi-orbital effects have a significant impact on a quantitative
level.
