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We consider a class of continuous generalized antiferromagnetic modelspreviously studied in \cite{Goldman-Runa} and \cite{Daneri-Runa}, and in thediscrete by \cite{Giuliani-Lebowitz-Lieb-Seiringer}. The functional consists ofan anisotropic perimeter term and a repulsive nonlocal term with a power lawkernel. In certain regimes the two terms enter in competition and symmetrybreaking with formation of periodic striped patterns is expected to occur. Inthis paper we extend the results of \cite{Daneri-Runa} to power law kernelswithin a range of exponents smaller than $d+2$, being $d$ the dimension of theunderlying space. In particular, we prove that in a suitable regime minimizersare periodic unions of stripes with a given optimal period. Notice that theexponent $d+1$ corresponds to an anisotropic version of the model for patternformation in thin magnetic films.

Striped patterns for generalized antiferromagnetic functionals with power law kernels of exponent smaller than $d+2$