We analyze how the logarithmic renormalizations in the Cooper channel affect the nonanalytic temperature dependence of the specific heat coefficient $\gamma \left(T\right)-\gamma \left(0\right)=A\left(T\right)T$ in a two-dimensional Fermi liquid. We show that $A\left(T\right)$ is expressed exactly in terms of the fully renormalized backscattering amplitude, which includes the renormalization in the Cooper channel. In contrast to the one-dimensional case, both charge and spin components of the backscattering amplitudes are subject to this renormalization. We show that the logarithmic renormalization of the charge amplitude vanishes for a flat Fermi surface when the system becomes effectively one dimensional.

• Received 25 April 2007

DOI:https://doi.org/10.1103/PhysRevB.76.165111