Anomalous self-energy and Fermi surface quasisplitting 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 two-particle 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 \omega\ less than or similar to Delta(0) near the Fermi level, where Delta(0) is the ground-state spin splitting. The spectral function at temperatures T less than or similar to Delta(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 << Delta(0). It is argued that this form of the spectral functions implies the quasisplitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations.