Dielectric response from lattices of dipoles with fixed orientation

The properties of dipolar cubic lattices are studied and the paradox of how to obtain a long range polarization in such lattices is resolved by choosing a proper shape of the total system. It has been shown that large but finite number of aligned dipoles prefer to exist as needle shaped macroscopic particles [M. Yoon and D. Tománek, J. Phys.: Condens. Matter 22, 455105 (2010)]. The total energy for a particle in such a system has one short range contribution depending on the packing (the chosen lattice) and one long range term depending on the dipole density of the system. We show that the latter term corresponds exactly to the polarization term from a dielectric medium embedding a sphere of the considered system. There is no need to include a dielectric medium in this modeling and the "dielectric stabilization" is generated solely by the dipoles of the system.