Arguin, L.-P.; C. M. Newman and D. L. Stein

An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then fluctuations in their energy differences — and therefore the possibility of multiple ground states — are closely related to the stability of their ground states. Here we examine the stability of ground states in two models, one of which is presumed to have a ground state structure that is qualitatively similar to other realistic short-range spin glasses in finite dimensions.