  We use scaling and renormalization-group techniques to analyze the leading
nonanalyticities in a Fermi liquid. We show that a physically motivated scaling
hypothesis reproduce the results known from perturbation theory for the density
of states, the density-of-states fluctuations, the specific heat, the spin
susceptibility, and the nematic magnetic susceptibility. We also discuss the
absence of nonanalytic terms in the density susceptibility. We then use a
recent effective field theory for clean electron systems to derive the scaling
hypothesis by means of renormalization-group techniques. This shows that the
exponents (although not the prefactors) of the nonanalyticities that were
previously derived by means of perturbative techniques are indeed exact, and
can be understood as the leading corrections to scaling at the stable
Fermi-liquid fixed point.
