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, presiously investigated by Kondor and Kondor and Végsö, 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. Unité propre du CNRS, associée à l’Ecole Normale Supérieure et à l’Université de Paris Sud 2 present address: NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark; e-mail: [email protected] Laboratoire associé au CNRS present address : Laboratoire de Physique, Ecole Normale Supérieure, 46 allées d’Italie, 69364 Lyon cedex 07, France