2021/01/08 by Alicja Kerschbaum, Kerschbaum, Alicja
Computer Science · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2101.02992
openalex publication_date 2021/01/08 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We consider a class of continuous generalized antiferromagnetic models previously studied in \citeGoldman-Runa and \citeDaneri-Runa, and in the discrete by \citeGiuliani-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 \citeDaneri-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.