ALT EDITORS' SUGGESTION Soft modes in vector spin glass models on sparse random graphs 23 January, 2025 The authors study here low-energy linear excitations in XY and Heisenberg spin glasses at zero temperature, considering systems defined on sparse random regular graphs. The localization properties of the soft modes are linked to the spin glass transition in a field. The authors discover a new kind of low-energy excitation, called a “Concentrated and Delocalized Low Energy Mode” (CDLEM), given that this excitation is restricted to a sub-extensive number of vertices spread over the largest possible distances. Silvio Franz et al. Phys. Rev. B 111, 014203 (2025)