Structure of correlations in three dimensional spin glasses

We investigate the low temperature phase of the three dimensional Edward-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 have power law decay. Our findings are in agreement with the replica symmetry breaking theory and show that the overlap is a good order parameter. © 2009 The American Physical Society.