Replica equivalence in the Edwards Anderson model

After introducing and discussing the link-overlap between spin configurations we show that the Edwards-Anderson model has a replica-equivalent quenched equilibrium state, a property introduced by Parisi in the description of the mean-field spin-glass phase which generalizes ultrametricity. Our method is based on the control of fluctuations through the property of stochastic stability and works for all the finite-dimensional spin-glass models.