  We extend Araki's well-known results on the equivalence of the KMS condition
and the variational principle for equilibrium states of quantum lattice systems
with short-range interactions, to a large class of models possibly containing
mean-field interactions (representing an extreme form of long-range
interactions). This result is reminiscent of van Hemmen's work on equilibrium
states for mean-field models. The extension was made possible by our recent
outcomes on states minimizing the free energy density of mean-field models on
the lattice, as well as on the infinite volume dynamics for such models.
