Verification of the proposed ground state for the aperiodic H_{1/2 1/2} artificial spin ice

Verify that the provisional ground-state configuration proposed for the aperiodic single-edge-length H_{1/2 1/2} artificial spin ice is a true ground state by analytically solving its proposed charge distributions using tiling substitution rules and conducting additional analysis in perpendicular space.

Background

The paper constructs a provisional ground-state configuration for the aperiodic H_{1/2 1/2} artificial spin ice by propagating low-energy vertex configurations across a local tiling patch. Unlike the periodic dice lattice, this proposed state necessarily contains specific excited 3i and 4i-b vertices because of the local geometric constraints and topological frustration of the aperiodic tiling.

The authors find that the proposed analytical configuration has slightly lower energy than the states obtained from their single-spin-flip Monte Carlo simulations, but emphasize that the construction has only been derived over a small patch. A complete verification therefore requires an analytic treatment of the charge distribution using substitution rules for the tiling, supplemented by perpendicular-space analysis, to establish whether the local construction extends to the full aperiodic system and is genuinely a ground state.

References

We note however that the ground state solution we show has fundamentally been derived only over a small patch of the $\psi_{-0.36}$ system. Future work aims to verify this configuration as a true ground state by analytically solving the proposed charge distributions using substitution rules, with additional analysis utilising perpendicular space.

— Artificial spin ice systems on single edge length tilings  (2608.20928 - Weightman et al., 21 Aug 2026) in Section III.2.2, “Quantitative analysis of the ground state solution”