Spin and Link Overlaps in Three-Dimensional Spin Glasses

Excitations of three-dimensional spin glasses are computed numerically. We find that one can flip a finite fraction of an $L\times L\times L$ lattice with an $O\left(1\right)$ energy cost, confirming the mean-field picture of a nontrivial spin overlap distribution $P\left(q\right)$. These low energy excitations are not domain-wall-like, rather they are topologically nontrivial and they reach out to the boundaries of the lattice. Their surface to volume ratios decrease as $L$ increases and may asymptotically go to zero. If so, link and window overlaps between the ground state and these excited states become “trivial.”