Corrections to Scaling are Large for Droplets in Two-Dimensional Spin Glasses

Abstract

The energy of a droplet of linear extent l in the droplet theory of spin glasses goes as l^θ for large l. It is shown by numerical studies of large droplets in two-dimensional systems that this formula needs to be modified by the addition of a scaling correction l^{-ω} in order to accurately describe droplet energies at the length scales currently probed in numerical simulations. Using this simple modification it is now possible to explain many results with the droplet model which have been found in simulations of three-dimensional Ising spin glasses.

4 pages, 2 figures, revtex

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• Energetics of clusters in the two-dimensional Ising spin glass
• Reduction of Two-Dimensional Dilute Ising Spin Glasses
• Local excitations in mean field spin glasses
• Excitations in high-dimensional random-field Ising magnets
• Replica-symmetry breaking for directed polymers
• On the Use of Finite-Size Scaling to Measure Spin-Glass Exponents
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