Low Energy Excitations in Spin Glasses from Exact Ground States

TL;DR

This study examines low-energy excitations in 3D spin glasses using exact ground states, revealing insights into their surface properties and scaling behavior, with implications for theoretical models like droplet and replica symmetry breaking.

Contribution

It provides the first exact ground state calculations for large 3D spin glasses and analyzes the nature of excitations, comparing different boundary conditions and correction to scaling effects.

Findings

Surface of excitations likely not space-filling

Energy scaling exponent ' compatible with zero

Algorithm performance correlates with large-scale excitations

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 \theta', 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.