Thermodynamic Limit for Mean-Field Spin Models

If the Boltzmann-Gibbs state of a mean-field N-particle system verifies a suitable subadditive condition for every possible decomposition of the system, 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.