Bilayer artificial spin ice: Magnetic force switching and basic thermodynamics

We study an artificial spin ice system consisting of two identical layers separated by a height offset $h$. For small separation, the are shown to attract each other, provided whole is in ground state. Such attraction comes about means power-law force that we compare van der Waals forces. When magnetic monopoles occur one (or both) layers, scenario becomes even more interesting and these may also repel other. By tuning parameters like $h$ monopole distance, switching between repulsion be accomplished feasible way. Regarding its thermodynamics, specific heat peak shifts lower temperature as increases.