Vortex ground state for small arrays of magnetic particles with dipole coupling

We show that a magnetic vortex is the ground state of an array of magnetic particles shaped as a hexagonal fragment of a triangular lattice, even for a small number of particles in the array N≤100. The vortex core appears and the symmetry of the vortex state changes with the increase of the intrinsic magnetic anisotropy of the particle β; the further increase of β leads to the destruction of the vortex state. Such vortices can be present in arrays as small in size as a dozen nanometers.