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Coherent vs incoherent pairing in 2D systems near magnetic instability

We study the superconductivity in 2D fermionic systems near antiferromagnetic instability, assuming that the pairing is mediated by spin fluctuations. This pairing involves fully incoherent fermions and diffusive spin excitations. We show that the competition between fermionic incoherence and strong pairing interaction yields the pairing instability temperature $T_{ins}$ which increases and saturates as the magnetic correlation length $ξ\to \infty$. We argue that in this quantum-critical regime the pairing problem is qualitatively different from the BCS one.