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

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.

10 pages, 11 figures. Replaced with published version

References in corpus (7)

• The two-dimensional random-bond Ising model, free fermions and the network model
• Lower Critical Dimension of Ising Spin Glasses
• Aspect-Ratio Scaling and The Stiffness Exponent $\theta$ for Ising Spin Glasses
• Non-compact local excitations in spin glasses
• Statistics of lowest droplets in two-dimensional Gaussian Ising spin glasses
• Statistics of lowest excitations in two dimensional Gaussian spin glasses
• Corrections to scaling in the droplet picture of spin glasses

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