Low Energy Excitations in Spin Glasses from Exact Ground States

Abstract

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, with only minimal corrections to scaling. When allowing for very large corrections to scaling, the data are also consistent with a picture with space-filling surfaces, such as replica symmetry breaking. The energy of the excitations scales with their size with a small exponent θ', which is compatible with zero if we allow moderate corrections to scaling. We compare the results with data for periodic boundary conditions obtained with a genetic algorithm, and discuss the effects of different boundary conditions on corrections to scaling. 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.

arXiv comment18 Revtex pages, 16 eps figures. Text significantly expanded with more discussion of the numerical data. Fig.11 added

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• Typical versus averaged overlap distribution in Spin-Glasses : Evidence for the droplet scaling theory
• The ground state energy of the Edwards-Anderson spin glass model with a parallel tempering Monte Carlo algorithm
• Influence of the Ground-State Topology on the Domain-Wall Energy in the Edwards-Anderson +/- J Spin Glass Model
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• Computational complexity of three-dimensional Ising spin glass: Lessons from D-Wave annealer
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