Large-Scale, Low-Energy Excitations in the Two-Dimensional Ising Spin Glass

TL;DR

This study investigates large-scale, low-energy excitations in 2D Ising spin glasses, supporting the droplet theory and analyzing finite-size effects with exact ground state calculations.

Contribution

It provides numerical evidence for the droplet theory in 2D spin glasses using exact ground state computations and examines finite-size scaling effects.

Findings

Results agree with droplet theory predictions

No evidence for theta' near -0.47 in small lattices

Finite-size effects are significant and require larger corrections

Abstract

We study large-scale, low-energy excitations in the Ising spin glass with Gaussian interactions in two-dimensions at zero temperature, using an optimization algorithm to determine exact ground states. Periodic boundary conditions are applied. Our results for the fractal dimension of the surface, d_s, and stiffness exponent, theta', for "droplet" excitations, are in reasonable agreement with estimates from "domain wall" calculations, and so support the predictions of the "droplet theory". Restricting our analysis to small lattices, we do not find an effective value of theta' close to -0.47 as has been recently proposed. The effects of averaging over droplets of different sizes are studied and are also found to be too small to give theta' approx -0.47 for smaller sizes. Larger corrections to finite-size scaling would be needed in three and four dimensions in order for the numerical data used to support the "TNT" scenario to be compatible with the droplet theory prediction that the stiffness exponent is the same for droplets and domain walls.