  At room temperature, PbTe and SnTe are efficient thermoelectrics with a cubic
structure. At low temperature, SnTe undergoes a ferroelectric transition with a
critical temperature strongly dependent on the hole concentration, while PbTe
is an incipient ferroelectric. By using the stochastic self-consistent harmonic
approximation, we investigate the anharmonic phonon spectra and the occurrence
of a ferroelectric transition in both systems. We find that vibrational spectra
strongly depends on the approximation used for the exchange-correlation kernel
in density functional theory. If gradient corrections and the theoretical
volume are employed, then the calculation of the free energy Hessian leads to
phonon spectra in good agreement with experimental data for both systems. In
PbTe, we reproduce the transverse optical mode phonon satellite detected in
inelastic neutron scattering and the crossing between the transverse optical
and the longitudinal acoustic modes along the $\Gamma$X direction. In the case
of SnTe, we describe the occurrence of a ferroelectric transition from the high
temperature Fm$\overline{3}$m structure to the low temperature R3m one.
