Low-temperature behavior of the spin overlap distribution in one-dimensional long-range diluted spin glasses

Computer simulations of the spin glass state find that the \emph{average} order parameter distribution $P(q)$ has a weight in the region of small overlap $q$ which does not appear to decrease with size for the range of sizes that can be studied. This is in agreement with the ``Replica Symmetry Breaking'' (RSB) picture as opposed to the droplet picture which predicts $P(0)=0$ in the thermodynamic limit. Recently, a detailed study [1] has been made of peaks in $P(q)$ for \emph{individual samples} of a three-dimensional spin glass to gain more understanding of the situation. Here we pursue a similar approach but for long-range models in one dimension for which the interactions fall off with a power of the distance. Varying the power is analogous to varying the space dimension of a short-range model, so we can conveniently study models which are proxies for a \emph{range} of space dimensions. We will present results on the nature of the peaks in $P(q)$ for individual samples for several such models, and interpret them in terms of the RSB and droplet pictures. References: [1] Phys. Rev. Lett. 109, 177204 (2012)