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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.
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