ON CHAOS IN MEAN-FIELD SPIN-GLASSES

We study the correlations between two equilibrium states of SK spin gl asses at different temperatures or magnetic fields. The question, prev iously investigated by Kondor and Kondor and Vegso, is approached here by constraining two copies of the same system at different external p arameters to have a fixed overlap. We find that imposing an overlap di fferent 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 a re completely uncorrelated. We also consider the generalized random en ergy model of Derrida as an example of a system with strong correlatio ns between states at different temperatures.