ON CHAOS IN MEAN-FIELD SPIN-GLASSES

We study the correlations between two equilibrium states of SK spin glasses at different temperatures or magnetic fields. The question, previously investigated by Kondor and Kondor and Vegso, is approached here by 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 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 a system with strong correlations between states at different temperatures.