Thermodynamic properties of Fermi systems with flat single-particle spectra

The behavior of strongly correlated Fermi systems is investigated beyond the onset of a phase transition where the single-particle spectrum $\xi({\bf p})$ becomes flat. The Landau-Migdal quasiparticle picture is shown to remain applicable on the ordered side of this transition. Nevertheless, low-temperature properties evaluated within this picture show profound changes relative to results of Landau theory, as a direct consequence of the flattening of $\xi({\bf p})$. Stability conditions for this class of systems are examined, and the nature of antiferromagnetic quantum phase transitions is elucidated.