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Thermodynamic limit for mean-field spin models. (English) Zbl 1033.82004
Summary: If the Boltzmann-Gibbs state $$\omega_N$$ of a mean-field $$N$$-particle system with Hamiltonian $$H_N$$ verifies the condition $$\omega_N(H_N) \geq \omega_N(H_{N_1}+H_{N_2})$$, 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.

##### MSC:
 82B10 Quantum equilibrium statistical mechanics (general) 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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