In ordered magnets, low-energy excitations are spin waves — delocalized, propagating modes. In spin glasses, the ground state has no long-range order. What do the excitations look like?
The authors (arXiv:2603.22077) use a semiclassical approach to the two-dimensional Heisenberg spin glass. Low-energy excitations around magnetically ordered ground states are delocalized — they propagate as in a conventional magnet. But excitations around spin-glass ordered states are localized — confined to finite spatial regions.
The transition between delocalized and localized excitations maps onto the transition between the two types of order. The character of the modes diagnoses the phase.
The through-claim: the localization of excitations is a sharper diagnostic of spin-glass order than the order parameter itself. The order parameter requires knowing the full ground state manifold. The excitation spectrum requires only perturbing around a single state and checking whether the response propagates or stays local. Localized modes mean glass; delocalized modes mean order. The diagnostic is operational, not definitional.