  We study effects of electron-electron interactions on the steady-state
characteristics of a hexagonal molecular ring in a magnetic field, as a model
for a benzene molecular junction. The system is driven out of equilibrium by
applying a bias voltage across two metallic leads. We employ a model
Hamiltonian approach to evaluate the effects of on-site as well as
nearest-neighbour density-density type interactions in a physically relevant
parameter regime. Results for the steady-state current, charge density and
magnetization in three different junction setups (para, meta and ortho) are
presented. Our findings indicate that interactions beyond the mean-field level
renormalize voltage thresholds as well as current plateaus. Electron-electron
interactions lead to substantial charge redistribution as compared to the
mean-field results. We identify a strong response of the circular current on
the electronic structure of the metallic leads. Our results are obtained by
steady-state Cluster Perturbation Theory, a systematically improvable
approximation to study interacting molecular junctions out of equilibrium, even
in magnetic fields. Within this framework general expressions for the current,
charge density and magnetization in the steady-state are derived. The method is
flexible and fast and can straight-forwardly be applied to effective models as
obtained from ab-initio calculations.
