Non-analytic magnetic field dependence of quasi-particle properties of two-dimensional metals

We show that in a weak external magnetic field H the quasi-particle residue and the renormalized electron Lande factor of two-dimensional Fermi liquids exhibit a non-analytic magnetic field dependence proportional to |H| which is due to electron-electron interactions. We explicitly calculate the corresponding prefactors to second order in the interaction and show that they are determined by low-energy scattering processes involving only momenta close to the Fermi surface. Experimentally, these non-analytic terms can be detected from measurements of the magnetic field dependence of the density of states and the magnetoconductivity.