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We consider the effect of perturbing a single bond on ground-states ofnearest-neighbor Ising spin-glasses, with a Gaussian distribution of thecoupling constants, across various two and three-dimensional lattices andregular random graphs. Our results reveal that the ground-states are strikinglysusceptible to such changes. Altering the strength of only a single bond beyonda critical threshold value leads to a new ground-state that differs from theoriginal one by a droplet of flipped spins whose boundary and volume divergewith the system size -- an effect that is reminiscent of the more familiarphenomenon of disorder chaos. These elementary fractal-boundary zero-energydroplets and their composites feature robust characteristics and provide thelowest-energy macroscopic spin-glass excitations. Remarkably, within numericalaccuracy, the size of such droplets conforms to a nearly universal power-lawdistribution with exponents dependent on the spatial dimension of the system.Furthermore, the critical coupling strengths adhere to a stretched Gaussiandistribution that is predominantly determined by the local coordination number.

Universal fragility of spin-glass ground-states under single bond changes