  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.
