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Analyticity in Hubbard models

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when βt is small, or βt^2/U is small; here, βis the inverse temperature, U the on-site repulsion and t the hopping coefficient. For more general models with Hamiltonian H = V + T where V involves local terms only, the free energy is analytic when β||T|| is small, irrespectively of V. The Gibbs state exists in the thermodynamic limit, is exponentially clustering and thermodynamically stable. These properties are rigorously established in this paper.