Finite lattice size effect in the ground state phase diagram of   quasi-two-dimensional magnetic dipolar dots array with perpendicular   anisotropy
  A prototype Hamiltonian for the generic patterned magnetic structures, of dipolar interaction with perpendicular anisotropy, is investigated within the finite-size framework by Landau-Lifshift-Gilbert classical spin dynamics. Modifications on the ground state phase diagram are discussed with an emphasis on the disappearance of continuous degeneracy in the ground state of in-plane phase due to the finite lattice size effect. The symmetry-governed ground state evolution upon the lattice size increase provides a critical insight into the systematic transition to the infinite extreme. 
R. H. He, X. F. Jin