Universal Fragility in the Response of Spin Glass Ground States to Single Bond Changes

We examine the effects of changing a single bond (local interaction) on the ground states of two- and three-dimensional Edwards-Anderson Ising spin glasses with a Gaussian distribution of coupling strengths. We find those ground states to be exceedingly fragile - altering the strength of only a single bond beyond a threshold value leads to a new ground state that differs from the original one by a cluster of flipped spins whose surface (contour) diverges with the volume of the system. These single contours provide the minimal-energy excitations of these spin glasses. Within our numerical accuracy, we find that the geometrical size of these excitations is governed by a nearly universal power-law distribution with exponents that depend only on the spatial dimension of the system. Further interesting properties of these excitations will also be discussed.