Thermodynamic limit for mean-field spin models

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) >= 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.