  We study the correlations between two equilibrium states of SK spin glasses
at different temperatures or magnetic fields. The question, presiously
investigated by Kondor and Kondor and V\'egs\"o, is approached here
constraining two copies of the same system at different external parameters to
have a fixed overlap. We find that imposing an overlap different from the
minimal one implies an extensive cost in free energy. This confirms by a
different method the Kondor's finding that equilibrium states corresponding to
different values of the external parameters are completely uncorrelated. We
also consider the Generalized Random Energy Model of Derrida as an example of
system with strong correlations among states at different temperatures.
