  Antiferromagnetic chains with an odd number of spins are known to undergo a
transition from an antiparallel to a spin-flop configuration when subjected to
an increasing magnetic field. We show that in the presence of an anisotropy
favoring alignment perpendicular to the field, the spin-flop state appears for
both weak and strong field, the antiparallel state appearing for intermediate
fields. Both transitions are second order, the configuration varying
continuously with the field intensity. Such re-entrant transition is robust
with respect to quantum fluctuations and it might be observed in different
types of nanomagnets.
