Analyticity in Hubbard models

The Hubbard model describes a lattice system of quantum particles with local ton-site) interactions. Its free energy is analytic when beta t is small, or beta t(2)/U is small; here, beta is 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 beta parallel to T parallel to is small, irrespective of V. There exists a unique Gibbs state showing exponential decay of spatial correlations. These properties are rigorously established in this paper.