Magnetostatic interaction fields for a three-dimensional array of ferromagnetic cubes

An exact analytic formula for the magnetostatic interaction energy of a three-dimensional array of ferromagnetic cubes is presented. The magnetization within each cube is assumed constant but varies in direction from cube to cube. From the expressions for the interaction energy, exact formulas for the effective magnetostatic interaction field are derived. This provides a useful tool for three-dimensional micromagnetic calculations.