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.
When a domain splits, the net decrease in energy equals the difference between the magnetic field energy saved and the additional energy required for the domain wall. The magnetic field energy scales with the cube of the domain's size, while the domain wall energy scales with the square of the domain's size.