  If the Boltzmann-Gibbs state $\omega_N$ of a mean-field $N$-particle system
with Hamiltonian $H_N$ verifies the condition $$ \omega_N(H_N) \ge
\omega_N(H_{N_1}+H_{N_2}) $$ for every decomposition $N_1+N_2=N$, then its free
energy density increases with $N$. We prove such a condition for a wide class
of spin models which includes the Curie-Weiss model, its p-spin generalizations
(for both even and odd p), its random field version and also the finite pattern
Hopfield model. For all these cases the existence of the thermodynamic limit by
subadditivity and boundedness follows.
