Low Energy Excitations in Spin Glasses from Exact Ground States

Matteo Palassini, Frauke Liers, Michael Jünger, and A.P. Young

We investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ``TNT'' picture. When allowing for large finite size correctios, the data are also consistent with a picture with space-filling surface, such as replica symmetry breaking. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on finite-size correction. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale, low-energy excitations.

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