High--frequency predictions for number counts and spectral properties of
  extragalactic radio sources. New evidences of a break at mm wavelengths in
  spectra of bright blazar sources
  We present models to predict high frequency counts of extragalactic radio
sources using physically grounded recipes to describe the complex spectral
behaviour of blazars, that dominate the mm-wave counts at bright flux
densities. We show that simple power-law spectra are ruled out by
high-frequency (nu>100 GHz) data. These data also strongly constrain models
featuring the spectral breaks predicted by classical physical models for the
synchrotron emission produced in jets of blazars (Blandford & Konigl 1979;
Konigl 1981). A model dealing with blazars as a single population is, at best,
only marginally consistent with data coming from current surveys at high radio
frequencies. Our most successful model assumes different distributions of break
frequencies, nu_M, for BL Lacs and Flat-Spectrum Radio Quasars (FSRQs). The
former objects have substantially higher values of nu_M, implying that the
synchrotron emission comes from more compact regions; therefore, a substantial
increase of the BL Lac fraction at high radio frequencies and at bright flux
densities is predicted. Remarkably, our best model is able to give a very good
fit to all the observed data on number counts and on distributions of spectral
indices of extragalactic radio sources at frequencies above 5 and up to 220
GHz. Predictions for the forthcoming sub-mm blazar counts from Planck, at the
highest HFI frequencies, and from Herschel surveys are also presented.
