Minimum Energy and Total Dipole Moment

Several magnetic materials consisting of dipoles owe their properties to the specific nature of the dipole–dipole interaction. In the present work, systems of particles possessing a dipole moment arranged on various types of 2D and 3D structures, completely arbitrary and, in some 2D instances, periodic (albeit finite), are studied. Noteworthy, the work is in the regime of strong dipole moments where a classical treatment is possible. The ultimate goal is to quantitatively address the unknown relation existing between the minimum possible energy of a system of dipoles and the concomitant total dipole moment. To such an end, classical numerical methods are used to the previous minimum energy–total dipole moment tandem for various magnetic configurations at zero temperature. An analytic bound for the minimal energy valid for any dimension is also obtained. With this exploration, new light is shed on the connection between the two former physical quantities, establishing an analytic inequality for particles, and describing other instances of physical interest.