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