  We consider a classical, two-dimensional system of identical particles which
interact via a finite-ranged, repulsive pair potential. We assume that the
system is in a crystalline phase. We calculate the normal vibrational modes of
a two-dimensional square Bravais lattice, first analytically within the
nearest-neighbour approximation, and then numerically, relaxing the preceding
hypothesis. We show that, in the harmonic approximation, the excitation of a
transverse vibrational mode leads to the breakdown of the square lattice. We
next study the case of the hexagonal Bravais lattice and we show that it can be
stable with respect to lattice vibrations. We give a criterion determining
whether or not it is stable in the nearest-neighbour approximation. Finally, we
apply our results to a two-dimensional system of composite bosons and infer
that the crystalline phase of such a system, if it exists, corresponds to a
hexagonal lattice.
