Non-compact local excitations in spin glasses

We study numerically the local low-energy excitations in the 3-d Edwards-Anderson model for spin glasses. Given the ground state, we determine the lowest-lying connected cluster of flipped spins with a fixed volume containing one given spin. These excitations are not compact, having a fractal dimension close to two, suggesting an analogy with lattice animals. Also, their energy does not grow with their size; the associated exponent is slightly negative whereas the one for compact clusters is positive. These findings call for a modification of the basic hypotheses underlying the droplet model.Comment: 7 pages, LaTex, discussion on stability clarifie

Energetics of clusters in the two-dimensional Ising spin glass

We study numerically the properties of local low-energy excitations in the two-dimensional Ising spin glass. Given the ground state, we determine the lowest-lying connected cluster of flipped spins containing one given spin, either with a fixed volume, or with a volume constrained to lie in a certain range. Our aim is to understand corrections to the scaling predicted by the droplet picture of spin glasses and to resolve contradictory results reported in the literature for the stiffness exponent. We find no clear trace of corrections to scaling, and the obtained stiffness exponent is in relatively good agreement with standard domain wall calculations.Comment: 8 pages, 9 figure