Numerical results for spin glass ground states on Bethe lattices:
Gaussian bonds |
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Authors: | S Boettcher |
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Institution: | 1.Physics Department,Emory University,Atlanta,USA |
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Abstract: | The average ground state energies for spin glasses on Bethe lattices
of connectivities r = 3,...,15 are studied numerically for a
Gaussian bond distribution. The Extremal Optimization heuristic is
employed which provides high-quality approximations to ground states.
The energies obtained from extrapolation to the thermodynamic limit
smoothly approach the ground-state energy of the
Sherrington-Kirkpatrick model for r ↦ ∞. Consistently for all
values of r in this study, finite-size corrections are found to
decay approximately with ~N-4/5. The possibility of ~N-2/3 corrections, found previously for Bethe lattices with a
bimodal ± J bond distribution and also for the
Sherrington-Kirkpatrick model, are constrained to the additional
assumption of very specific higher-order terms. Instance-to-instance
fluctuations in the ground state energy appear to be asymmetric up to
the limit of the accuracy of our heuristic. The data analysis
provides insights into the origin of trivial fluctuations when using
continuous bonds and/or sparse networks. |
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Keywords: | |
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