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In this paper we continue our analysis of the interplay between the pairing and the non-Fermi liquid behavior in a metal for a set of quantum-critical models with an effective dynamical electron-electron interaction V(Ωm)∝1/|Ωm|γ (the γ model). We analyze both the original model and its extension, in which we introduce an extra parameter N to account for nonequal interactions in the particle-hole and particle-particle channel. In two previous papers [A. Abanov and A. V. Chubukov, Phys. Rev. B 102, 024524 (2020) and Y. Wu et al. Phys. Rev. B 102, 024525 (2020)] we considered the case 0<γ<1 and argued that (i) at T=0, there exists an infinite discrete set of topologically different gap functions Δn(ωm), all with the same spatial symmetry, and (ii) each Δn evolves with temperature and terminates at a particular Tp,n. In this paper we analyze how the system behavior changes between γ<1 and γ>1, both at T=0 and a finite T. The limit γ→1 is singular due to infrared divergence of ∫dωmV(Ωm), and the system behavior is highly sensitive to how this limit is taken. We show that for N=1, the divergencies in the gap equation cancel out, and Δn(ωm) gradually evolve through γ=1 both at T=0 and a finite T. For N≠1, divergent terms do not cancel, and a qualitatively new behavior emerges for γ>1. Namely, the form of Δn(ωm) changes qualitatively, and the spectrum of condensation energies Ec,n becomes continuous at T=0. We introduce different extension of the model, which is free from singularities for γ>1. 

The proximity of many strongly correlated superconductors to density-wave or nematic order has led to an extensive search for fingerprints of pairing mediated by dynamical quantum-critical (QC) fluctuations of the corresponding order parameter. Here we study anisotropics-wave superconductivity induced by anisotropic QC dynamical nematic fluctuations. We solve the non-linear gap equation for the pairing gap$$\Delta (\theta ,{\omega }_{m})$$$\Delta \left(\theta ,{\omega }_m\right)$and show that its angular dependence strongly varies below$${T}_{{\rm{c}}}$$$T_c$. We show that this variation is a signature of QC pairing and comes about because there are multiples-wave pairing instabilities with closely spaced transition temperatures$${T}_{{\rm{c}},n}$$$T_{c,n}$. Taken alone, each instability would produce a gap$$\Delta (\theta ,{\omega }_{m})$$$\Delta \left(\theta ,{\omega }_m\right)$that changes sign$$8n$$$8n$times along the Fermi surface. We show that the equilibrium gap$$\Delta (\theta ,{\omega }_{m})$$$\Delta (\theta ,{\omega }_m)$is a superposition of multiple components that are nonlinearly induced below the actual$${T}_{{\rm{c}}}={T}_{{\rm{c}},0}$$$T_c=T_{c,0}$, and get resonantly enhanced at$$T={T}_{{\rm{c}},n}\ <\ {T}_{{\rm{c}}}$$$T=T_{c,n}<T_c$. This gives rise to strong temperature variation of the angular dependence of$$\Delta (\theta ,{\omega }_{m})$$$\Delta \left(\theta ,{\omega }_m\right)$. This variation progressively disappears away from a QC point.