On the structure of correlations in the three dimensional spin glasses

We investigate the low temperature phase of three-dimensional Edwards-Anderson model with Bernoulli random couplings. We show that at a fixed value $Q$ of the overlap the model fulfills the clustering property: the connected correlation functions between two local overlaps decay as a power whose exponent is independent of $Q$ for all $0\le \mathrm{\mid }Q\mathrm{\mid }<q_{EA}$. Our findings are in agreement with the RSB theory and show that the overlap is a good order parameter.