Presence versus absence of two-dimensional Fermi surface anomalies

We theoretically consider Fermi surface anomalies manifesting in the temperature dependent quasiparticle properties of two-dimensional (2D) interacting electron systems, comparing and contrasting with corresponding 3D liquid situation. In particular, employing microscopic many body perturbative techniques, we obtain analytically leading-order next-to-leading-order interaction corrections to renormalized effective mass for three distinct physical models: electron-phonon, electron-paramagnon, electron-electron Coulomb coupling. find that 2D does not develop any anomaly due electron-phonon interaction, $\mathcal{O}(T^2)$ correction thus remaining consistent Sommerfeld expansion non-interacting function, contrast situation where has anomalous $T^2 \log T$ behavior. By contrast, both electron-paramagnon interactions lead $\mathcal{O}(T)$ renormalization behavior systems. provide detailed analytical results, comment on conditions under which a term could possibly arise from interactions. also compare results specific heat using close connection between heat.