  We consider a class of continuous generalized antiferromagnetic models
previously studied in \cite{Goldman-Runa} and \cite{Daneri-Runa}, and in the
discrete by \cite{Giuliani-Lebowitz-Lieb-Seiringer}. The functional consists of
an anisotropic perimeter term and a repulsive nonlocal term with a power law
kernel. In certain regimes the two terms enter in competition and symmetry
breaking with formation of periodic striped patterns is expected to occur. In
this paper we extend the results of \cite{Daneri-Runa} to power law kernels
within a range of exponents smaller than $d+2$, being $d$ the dimension of the
underlying space. In particular, we prove that in a suitable regime minimizers
are periodic unions of stripes with a given optimal period. Notice that the
exponent $d+1$ corresponds to an anisotropic version of the model for pattern
formation in thin magnetic films.
