Abstract
We use a sample-dependent analysis, based on medians and quantiles, to analyze the behavior of the overlap probability distribution of the Sherrington-Kirkpatrick and $3D$ Edwards-Anderson models of Ising spin glasses. We find that this approach is an effective tool to distinguish between replica symmetry breaking--like and droplet-like behavior of the spin-glass phase. Our results are in agreement with a replica symmetry breaking--like behavior for the $3D$ Edwards-Anderson model.
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