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 an small number of particles in the array \(N \leq 100\). The vortex core appears and the symmetry of the vortex state changes with the increase of the intrinsic magnetic anisotropy of the particle \(\beta\); the further increase of \(\beta\) leads to the destruction of the vortex state. Such vortices can be present in arrays as small in size as dozen of nanometers.