  We consider the effect of perturbing a single bond on ground-states of
nearest-neighbor Ising spin-glasses, with a Gaussian distribution of the
coupling constants, across various two and three-dimensional lattices and
regular random graphs. Our results reveal that the ground-states are strikingly
susceptible to such changes. Altering the strength of only a single bond beyond
a critical threshold value leads to a new ground-state that differs from the
original one by a droplet of flipped spins whose boundary and volume diverge
with the system size -- an effect that is reminiscent of the more familiar
phenomenon of disorder chaos. These elementary fractal-boundary zero-energy
droplets and their composites feature robust characteristics and provide the
lowest-energy macroscopic spin-glass excitations. Remarkably, within numerical
accuracy, the size of such droplets conforms to a nearly universal power-law
distribution with exponents dependent on the spatial dimension of the system.
Furthermore, the critical coupling strengths adhere to a stretched Gaussian
distribution that is predominantly determined by the local coordination number.

Disordered Systems and Neural Networks;Statistical Mechanics