  We determine the effective dipolar interaction between single domain
two-dimensional ferromagnetic particles (islands or dots), taking into account
their finite size. The first correction term decays as 1/D^5, where D is the
distance between particles. If the particles are arranged in a regular
two-dimensional array and are magnetized in plane, we show that the correction
term reinforces the antiferromagnetic character of the ground state in a square
lattice, and the ferromagnetic one in a triangular lattice. We also determine
the dipolar spin-wave spectrum and evaluate how the Curie temperature of an
ensemble of magnetic particles scales with the parameters defining the particle
array: height and size of each particle, and interparticle distance. Our
results show that dipolar coupling between particles might induce ferromagnetic
long range order at experimentally relevant temperatures. However, depending on
the size of the particles, such a collective phenomenon may be disguised by
superparamagnetism.
