  Magnetic superlattices and nanowires may be described as Heisenberg spin
chains of finite length N, where N is the number of magnetic units (films or
atoms, respectively). We study antiferromagnetically coupled spins which are
also coupled to an external field H (superlattices) or to a ferromagnetic
substrate (nanowires). The model is analyzed through a two-dimensional map
which allows fast and reliable numerical calculations. Both open and closed
chains have different properties for even and odd N (parity effect). Open
chains with odd N are known [S.Lounis et al., Phys. Rev. Lett. 101, 107204
(2008)] to have a ferrimagnetic state for small N and a noncollinear state for
large N. In the present paper, the transition length N_c is found analytically.
Finally, we show that closed chains arrange themselves in the uniform bulk
spin-flop state for even N and in nonuniform states for odd N.
