Finite-temperature contributions to the magnetic susceptibility of a normal Fermi liquid

We show that long-wavelength spin and density fluctuations give no $T^2\ln T$ contribution to the magnetic susceptibility of a normal Fermi liquid. The calculations are made within the framework of Landau Fermi-liquid theory. We find that while there are $T^2\ln T$ terms arising from both the quasiparticle density of states and from the Landau quasiparticle interaction function, their sum vanishes. In calculating the Landau quasiparticle interaction, it is found to be important to include processes involving two long-wavelength fluctuations, in addition to the exchange of a single fluctuation.