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We perform an instability analysis of the Emery three-band model at holedoping and weak coupling within a channel-decomposed functional renormalizationgroup flow proposed in Phys. Rev. B 79, 195125 (2009). In our approach,momentum dependences are taken into account with improved precision compared toprevious studies of related models. Around a generic parameter set, we find astrong competition of antiferromagnetic and d-wave Cooper instabilities with asmooth 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 theEmery model to those obtained for the two-dimensional one-band Hubbard modelwith effective parameters, we find that, despite considerable qualitativeagreement, multi-orbital effects have a significant impact on a quantitativelevel.

Multiorbital effects in the functional renormalization group: A weak-coupling study of the Emery model