  By using a simple interpolation argument, in previous work we have proven the
existence of the thermodynamic limit, for mean field disordered models,
including the Sherrington-Kirkpatrick model, and the Derrida p-spin model. Here
we extend this argument in order to compare the limiting free energy with the
expression given by the Parisi Ansatz, and including full spontaneous replica
symmetry breaking. Our main result is that the quenched average of the free
energy is bounded from below by the value given in the Parisi Ansatz uniformly
in the size of the system. Moreover, the difference between the two expressions
is given in the form of a sum rule, extending our previous work on the
comparison between the true free energy and its replica symmetric
Sherrington-Kirkpatrick approximation. We give also a variational bound for the
infinite volume limit of the ground state energy per site.
