Finite dipolar hexagonal columns on piled layers of triangular lattice
  We have investigated, by the Monte Carlo simulation, spin systems which represent moments of arrayed magnetic nanoparticles interacting with each other only by the dipole-dipole interaction. In the present paper we aim the understanding of finite size effects on the magnetic nanoparticles arrayed in hexagonal columns cut out from the close-packing structures or from those with uniaxial compression. In columns with the genuine close-packing structures, we observe a single vortex state which is also observed previously in finite 2-dimensional systems. On the other hand in the system with the inter-layer distance set $1/\sqrt{2}$ times of the close-packing one, we found ground states which depend on the number of layers. The dependence is induced by a finite size effect and is related to a orientation transition in the corresponding bulk system. 
Katsuyoshi Matsushita, Ryoko Sugano, Akiyoshi Kuroda, Yusuke Tomita,   Hajime Takayama