Physics of the Edwards-Anderson Spin Glass in Dimensions $d=3,\ldots,8$ from Heuristic Ground State Optimization

We present a collection of simulations of the Edwards-Anderson lattice spin glass at $T=0$ to elucidate the nature of low-energy excitations over a range of dimensions that reach from physically realizable systems to the mean-field limit. Using heuristic methods, we sample ground states of instances to determine their energies while eliciting excitations through manipulating boundary conditions. We exploit the universality of the phase diagram of bond-diluted lattices to make such a study in higher dimensions computationally feasible. As a result, we obtain a verity of accurate exponents for domain wall stiffness and finite-size corrections that allow us to examine their dimensional behavior and their connection with predictions from mean-field theory. We also provide an experimentally testable prediction for the thermal-to-percolative crossover exponent in dilute lattices Ising spin glasses.