Low-energy excitations and local hardness in spin glasses

In this talk I will provide an overview over the role of excitations in spin glasses and discuss ways of how they could be probed in numerical simulations. In contrast to much of the prior work, I will consider the effect of perturbing a single bond on ground states of nearest-neighbor Ising spin glasses on a wide range of lattices and graphs, revealing that the ground states are strikingly fragile with respect to such changes. The resulting excitations are extensive with fractal boundaries, but bounded in energy, hence combining properties usually attributed to the droplet and replica-symmetry breaking pictures of the spin-glass transition. The existence of threshold instabilities triggering such excitations is connected to the 'local hardness' of finding spin-glass ground states. I will present results relating to the efficiency of local predictors of relative spin orientations, which we find to be closely related to the occurrence of such instabilities. Away from criticality, local solvers quickly achieve high accuracy, aligning closely with the results of the more computationally intensive global minimization. Depending on the model considered, we observe varying scaling behaviors in how errors associated with local predictions decay as a function of the size of the solved subsystem, thus suggesting the existence of various classes of local hardness.