  The nature of the spin glass state is investigated by studying changes to the
ground state when a weak perturbation is applied to the bulk of the system. We
consider short range models in three and four dimensions and the infinite range
Sherrington-Kirkpatrick (SK) and Viana-Bray models. Our results for the SK and
Viana-Bray models agree with the replica symmetry breaking picture. The data
for the short range models fit naturally a picture in which there are large
scale excitations which cost a finite energy but whose surface has a fractal
dimension, $d_s$, less than the space dimension $d$. We also discuss a possible
crossover to other behavior at larger length scales than the sizes studied.
