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We consider a classical, two-dimensional system of identical particles whichinteract via a finite-ranged, repulsive pair potential. We assume that thesystem is in a crystalline phase. We calculate the normal vibrational modes ofa two-dimensional square Bravais lattice, first analytically within thenearest-neighbour approximation, and then numerically, relaxing the precedinghypothesis. We show that, in the harmonic approximation, the excitation of atransverse vibrational mode leads to the breakdown of the square lattice. Wenext study the case of the hexagonal Bravais lattice and we show that it can bestable with respect to lattice vibrations. We give a criterion determiningwhether or not it is stable in the nearest-neighbour approximation. Finally, weapply our results to a two-dimensional system of composite bosons and inferthat the crystalline phase of such a system, if it exists, corresponds to ahexagonal lattice.

Harmonic Stability Analysis of the 2D Square and Hexagonal Bravais  Lattices for a Finite--Ranged Repulsive Pair Potential. Consequence for a 2D  System of Ultracold Composite Bosons