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We revisit the metastability properties of the mixed p-spin sphericaldisordered models. Firstly, using known methods, we show that there istemperature chaos in a broad range of temperatures. Secondly, we modify thedefinition of the Thouless-Anderson-Palmer free energy density by includingconstraints that enforce a chosen overlap between the searched metastablestates and another reference state, that could be a characteristic one of adifferent temperature. We argue that this refined analysis provides clues tounderstand the weird behaviour of the low temperature relaxation dynamics ofthese models, and suggests ways to improve the treatment of the initialconditions to overcome the difficulties encountered so far.

A constrained TAP approach for disordered spin models: application to the mixed spherical case