  It is well known that the flat radio spectrum is a common property in the
spectral energy distribution of blazars. Although the one-zone leptonic models
are generally successful in explaining the multi-wave band emission, they are
problematic in reproducing the radio spectrum. In the study of Mrk 421,
one-zone models suggest that in order to avoid overproducing the radio flux,
the minimum electron Lorentz factor should be larger than a few hundred at
least, even considering the synchrotron self-absorption effect. This result
suggests that the model predicted spectral index in the radio band of Mrk 421
should be -1/3. On the basis of this result, by assuming there is a neglected
region that will also contribute the radio emission and its electron energy
index is naturally originate from the simplest first-order Fermi acceleration
mechanism, we can get a superimposed flat radio spectrum. In this paper, a
two-zone model is proposed to reproduce the quiescent state spectral energy
distribution of Mrk 421. In addition to taking into account the emission from a
conventional radiation zone, we further consider the emission from the
acceleration zone in which particles are accelerated at a shock front. With the
present model, our fitting result suggests that the low frequency flat radio
spectrum of Mrk 421 might be explained as a superposition of the synchrotron
emission from acceleration zone and radiation zone.
