  At the core of every frustrated system, one can identify the existence of
frustrated rings that are usually interpreted in terms of single--particle
physics. We check this point of view through a careful analysis of the
entanglement entropy of both models that admit an exact single--particle
decomposition of their Hilbert space due to integrability and those for which
the latter is supposed to hold only as a low energy approximation. In
particular, we study generic spin chains made by an odd number of sites with
short-range antiferromagnetic interactions and periodic boundary conditions,
thus characterized by a weak, i.e. nonextensive, frustration. While for
distances of the order of the correlation length the phenomenology of these
chains is similar to that of the non-frustrated cases, we find that correlation
functions involving a number of sites scaling like the system size follow
different rules. We quantify the long-range correlations through the von
Neumann entanglement entropy, finding that indeed it violates the area law,
while not diverging with the system size. This behavior is well fitted by a
universal law that we derive from the conjectured single--particle picture.
