Low-energy excitations in spin glasses from exact ground states

Palassini M, Liers F, Jünger M, Young AP (2003)

Publication Status: Published

Publication Type: Journal article, Original article

Publication year: 2003


Publisher: American Physical Society

Book Volume: 68

Pages Range: 644131-6441316

Article Number: 064413

Journal Issue: 6

URI: https://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=0141839746&origin=inward


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 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 trivial-non-trivial (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.

Authors with CRIS profile

Involved external institutions

How to cite


Palassini, M., Liers, F., Jünger, M., & Young, A.P. (2003). Low-energy excitations in spin glasses from exact ground states. Physical Review B, 68(6), 644131-6441316.


Palassini, Matteo, et al. "Low-energy excitations in spin glasses from exact ground states." Physical Review B 68.6 (2003): 644131-6441316.

BibTeX: Download