Anomalous self-energy and Fermi surface quasi-splitting in the vicinity of a ferromagnetic instability

We discuss the low-temperature behavior of the electronic self-energy in the vicinity of a ferromagnetic instability in two dimensions within the twoparticle self-consistent approximation, functional renormalization group and Ward-identity approaches. Although the long-range magnetic order is absent at T > 0, the self-energy has a non-Fermi liquid form at low energies |ω| . ∆0 near the Fermi level, where ∆0 is the ground-state spin splitting. The spectral function at temperatures T . ∆0 has a two-peak structure with finite spectral weight at the Fermi level. The simultaneous inclusion of self-energy and vertex corrections shows that the above results remain qualitatively unchanged down to very low temperatures T ≪ ∆0. It is argued, that this form of the spectral functions implies the quasi-splitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations.