  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 argument is based on the control of fluctuations through
the property of stochastic stability and works for all the finite-dimensional
spin-glass models.
