  Are solids intrinsically different from liquids? Must a finite stress be
applied in order to induce flow? Or, instead, do all solids only look rigid on
some finite timescales and eventually flow if an infinitesimal shear stress is
applied? Surprisingly, these simple questions are a matter of debate and
definite answers are still lacking. Here we show that solidity is only a
time-scale dependent notion: equilibrium states of matter that break
spontaneously translation invariance, e.g. crystals, flow if even an
infinitesimal stress is applied. However, they do so in a way inherently
different from ordinary liquids since their viscosity diverges for vanishing
shear stress with an essential singularity. We find an ultra-slow decrease of
the shear stress as a function of the shear rate, which explains the apparent
yield stress identified in rheological flow curves. Furthermore, we suggest
that an alternating shear of frequency $\omega$ and amplitude $\gamma$ should
lead to a dynamic phase transition line in the ($\omega$,$\gamma$) plane, from
a 'flowing' to a 'non-flowing' phase. Finally, we apply our results to
crystals, show the corresponding microscopic process leading to flow and
discuss possible experimental investigations.
