Francesco Guerra
ABOUT THE OVERLAP DISTRIBUTION IN MEAN FIELD SPIN GLASS MODELS
(26K, TeX)

ABSTRACT.  We continue our presentation of mathematically rigorous results about the
Sherrington-Kirkpatrick mean field spin glass model. Here we establish some
properties of the distribution of overlaps between real replicas. They are in
full agreement with the Parisi accepted picture of spontaneous replica symmetry
breaking. As a byproduct, we show that the selfaveraging of the
Edwards-Anderson fluctuating order parameter, with respect to the external
quenched noise, implies that the overlap distribution is given by the
Sherrington-Kirkpatrick replica symmetric Ansatz. This extends previous
results of Pastur and Shcherbina. Finally, we show how to generalize our
results to realistic short range spin glass models.