  We introduce a diagrammatic formulation for a cavity field expansion around
the critical temperature. This approach allows us to obtain a theory for the
overlap's fluctuations and, in particular, the linear part of the
Ghirlanda-Guerra relationships (GG) (often called Aizenman-Contucci polynomials
(AC)) in a very simple way. We show moreover how these constraints are
"superimposed" by the symmetry of the model with respect to the restriction
required by thermodynamic stability. Within this framework it is possible to
expand the free energy in terms of these irreducible overlaps fluctuations and
in a form that simply put in evidence how the complexity of the solution is
related to the complexity of the entropy.
