  We study the scaling properties of the ground-state entanglement between
finite subsystems of infinite two-dimensional free lattice models, as measured
by the logarithmic negativity. For adjacent regions with a common boundary, we
observe that the negativity follows a strict area law for a lattice of harmonic
oscillators, whereas for fermionic hopping models the numerical results
indicate a multiplicative logarithmic correction. In this latter case, we
conjecture a formula for the prefactor of the area-law violating term, which is
entirely determined by the geometries of the Fermi surface and the boundary
between the subsystems. The conjecture is tested against numerical results and
a good agreement is found.
