White and weighted averages over solutions of Thouless Anderson Palmer equations for the Sherrington Kirkpatrick spin glass

We study white and weighted averages of observables over all solutions of Thouless Anderson and Palmer equations. For the white average we give analytic results near the transition temperature and near T = 0, in good qualitative agreement with expected results for the Edwards Anderson order parameter. A too high value for the ground state energy is attributed to the non discriminating character of the white average. Local stability in all directions is verified for the relevant saddle point (diagonal in replica space). We also study a microcanonical average at T = 0. In that case, the diagonal saddle point is unstable and equations for the off-diagonal one are not soluble by purely analytical means.