Thus the net amount that the energy is reduced when a domain splits is equal to the difference between the magnetic field energy saved, and the additional energy required to create the domain wall. The field energy is proportional to the cube of the domain size, while the domain wall energy is proportional to the square of the domain size.
The reduction in energy when a domain splits is equal to the difference between the magnetic field energy saved and the extra energy needed for the domain wall. Both the magnetic field energy and the domain wall energy are proportional to the dimensions of the domain, though their relationships differ (magnetic field energy cubed vs. domain size squared).