WHITE AND WEIGHTED AVERAGES OVER SOLUTIONS OF PALMER,THOULESS,ANDERSON EQUATIONS FOR THE KIRKPATRICK,SHERRINGTON SPIN-GLASS

White and weighted averages of observables over all solutions of Thouless Anderson and Palmer equations are studied, giving analytic results for the white average near the transition temperature and near T equals 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). Also studied is a microcanonical average at T equals 0. In that case, the diagonal saddle point is unstable and equations for the off-diagonal one are not soluble by purely analytical means.