Nonanalytic corrections to the specific heat and susceptibility of a non-Galilean-Invariant Two-Dimensional Fermi Liquid

We consider the leading non-analytic temperature dependence of the specific heat and temperature and momentum dependence of the spin susceptibility for two dimensional fermionic systems with non-circular Fermi surfaces. We demonstrate the crucial role played by Fermi surface curvature. For a Fermi surface with inflection points, we demonstrate that thermal corrections to the uniform susceptibility in D=2 change from $\chi_{s} \propto T$ to $\chi_{s} \propto T^{2/3}$ for generic inflection points, and to $\chi_{s} \propto T^{1/2}$ for special inflection points along symmetry directions. Errors in previous work are corrected. Application of the results to $Sr_2RuO_4$ is given.