  The dispersion relations of collective oscillations of the magnetic moment of
magnetic dots arranged in square-planar arrays and having magnetic moments
perpendicular to the array plane are calculated. The presence of the external
magnetic field perpendicular to the plane of array, as well as the uniaxial
anisotropy for single dot are taken into account. The ferromagnetic state with
all the magnetic moments parallel, and chessboard antiferromagnetic state are
considered. The dispersion relation yields information about the stability of
different states of the array. There is a critical magnetic field below which
the ferromagnetic state is unstable. The antiferromagnetic state is stable for
small enough magnetic fields. The dispersion relation is non-analytic as the
value of the wave vector approaches zero. Non-trivial Van Hove anomalies are
also found for both ferromagnetic and antiferromagnetic states.
