Two-dimensional model

By considering only two-dimensional cut-planes of the hexagonal antispheres -- assuming that the individual layers behave independently -- it is possible to simulate significantly larger systems in the $x$ and $y$ directions than if attempting to perform a simulation across a three-dimensional sample of similar proportions. We can then measure the coercive field for different layers.

The hexagonal antisphere systems in Zhukov et al. (2003) can be mapped to
two-dimensional samples by considering hexagonally-spaced circular holes -- flat antidots -- in a thin film. By varying the ratio of hole radius $r$ to spacing radius $R$ the surface of the antisphere geometry at different heights can be modelled reasonably accurately. Since larger systems can be simulated, the influence of the sample edges detailed in section 6.3 is substantially reduced (figure 6.6).