  We discuss in this study the possibility of finding a finite mass gap in the
broken phase of the sine-Gordon model in $d=2$ using the functional flows. We
demonstrate that the signal of the presence of massive excitations, a finite
positively-curved {\em blocked} potential around its minima, is recovered only
in our treatment. The usual results based on the flow of the Fourier expansion
of the {\em blocked} action are then shown to actually fit a singularity.
