Corrections to Fermi Liquid theory in 2D in a magnetic field

In this work, we consider a Fermi liquid in two dimensions in a magnetic field, and study the effects of the Zeeman splitting on thermodynamics. We derive the temperature dependence of the spin susceptibility $\chi_s (T)$ from the thermodynamic potential, and show explicitly how $2p_F$ scattering gives rise to a non- analytic temperature dependence of the susceptibility. We explain why small momentum scattering does not give rise to non-analytic $\chi_s (T)$. We discuss experimental implications of this result.