  We present a simple strategy in order to show the existence and uniqueness of
the infinite volume limit of thermodynamic quantities, for a large class of
mean field disordered models, as for example the Sherrington-Kirkpatrick model,
and the Derrida p-spin model. The main argument is based on a smooth
interpolation between a large system, made of N spin sites, and two similar but
independent subsystems, made of N_1 and N_2 sites, respectively, with
N_1+N_2=N. The quenched average of the free energy turns out to be subadditive
with respect to the size of the system. This gives immediately convergence of
the free energy per site, in the infinite volume limit. Moreover, a simple
argument, based on concentration of measure, gives the almost sure convergence,
with respect to the external noise. Similar results hold also for the ground
state energy per site.
