  A thermodynamic stability criterion for the spontaneous breaking of the
translation invariance of many particle systems is derived. It simply requires
the positive character of the wavevector dependent dielectric function as
generalising the same condition for macroscopic dielectric constants. Its
application to the Single Mode Approximation (SMA) for the description of the
collective modes of the filling factor 1/m Laughlin states is considered. The
results indicate that the stability condition is violated by the SMA for all
the relevant states m=3,5,7,9 in a wavevector neighborhood of the magneto-roton
minima. These conclusions are in qualitative agreement with similar results
obtained from the solution of the Bethe-Salpeter equation at 1/3 filling factor
for both composite fermions and phenomenologically described electrons in the
Laughlin state.
