  The low-temperature properties of the so-called ''charge ordered'' state in
50% doped perovskite manganites are described from the viewpoint of the
magnetic spin ordering. In these systems, the zigzag antiferromagnetic
ordering, combined with the double-exchange physics, effectively divides the
whole sample into the one-dimensional ferromagnetic zigzag chains and results
in the anisotropy of electronic properties. The electronic structure of one
such chain is described by an effective 3$\times$3 Hamiltonian in the basis of
Mn($3de_g$) orbitals. We treat this problem analytically and consider the
following properties: (i) the nearest-neighbor magnetic interactions; (ii) the
distribution of the Mn($3de_g$) and Mn($4p$) states near the Fermi level, and
their contribution to the optical conductivity and the resonant x-ray
scattering near the Mn $K$-absorption edge. We argue that the anisotropy of
magnetic interactions in the double-exchange limit, combined with the isotropic
superexchange interactions, readily explains both the local and the global
stability of the zigzag antiferromagnetic state. The two-fold degeneracy of
$e_g$ levels plays a very important role in the problem and explains the
insulating behavior of the zigzag chain, as well as the appearance of the
orbital ordering in the double-exchange model. Importantly, however, the charge
ordering itself is expected to play only a minor role and is incompatible with
the ferromagnetic coupling within the chain. We also discuss possible effects
of the Jahn-Teller distortion and compare the tight-binding picture with
results of band structure calculations in the local-spin-density approximation.
