Quasi-uniform in plane magnetization state of thin cylindrical dots in a   square array and related anisotropy
  The energy (magnetostatic, exchange and Zeeman terms) of a square array of cylindrical sub-micron dots made of soft ferromagnetic material is calculated analytically and minimized, taking into account quasi-uniformity of dots magnetization. The dependence of the equilibrium energy of the array on the direction of the externally applied magnetic field in the array plane is recovered, exhibiting the four-fold anisotropy. The anisotropy constant is calculated. Its values for different array geometries are in excellent agreement to the recent independent experiments. New eight-fold anisotropy effect is predicted. Theory involves no adjustable parameters. 
Konstantin L. Metlov