Numerical study of the two-replica overlap of the 3D Edwards–Anderson Ising spin glass

We present results of recent high-statistics Monte Carlo simulations of the Edwards–Anderson Ising spin-glass model in three dimensions. The study is based on a non-Boltzmann sampling technique, the multi-self-overlap algorithm which is specifically tailored for sampling rare-event states. We thus concentrate on those properties which are difficult to obtain with standard canonical Boltzmann sampling such as the free-energy barriers FBq in the probability densities PJ(q) of the Parisi overlap parameter q and the behavior of the tails of the disorder averaged density P(q)=[PJ(q)]av. Our results for the tails disagree with mean-field predictions and support extreme order statistics over many orders of magnitude.