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

A.K. Hartmann and A.P. Young
Phys. Rev. B 66, 094419 (2002), cond-mat/0205659

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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