Published Paper

Inserted: 11 feb 2026
Last Updated: 11 feb 2026

Journal: Calc. Var. PDE
Year: 2022
Doi: DOI:10.1007/s00526-021-02120-4

Abstract:

In this paper we consider the diffuse interface generalized antiferromagnetic model with localnonlocal attractiverepulsive terms in competition studied in Daneri-Kerschbaum-Runa arXiv:1907.06419. The parameters of the model are denoted by $τ$ and $\varepsilon$: the parameter $τ$ represents the relative strength of the local term with respect to the nonlocal one, while the parameter $\varepsilon$ describes the transition scale in the Modica-Mortola type term. Restricting to a periodic box of size $L$, with $L$ multiple of the period of the minimal one-dimensional minimizers, in Daneri-Kerschbaum-Runa arXiv:1907.06419 the authors prove that in any dimension $d\geq1$ and for small but positive $τ$ and $\varepsilon$ (eventually depending on $L$), the minimizers are non-constant one-dimensional periodic functions. In this paper we prove that periodicity and one-dimensionality of minimizers occurs also in the zero temperature analogue of the thermodynamic limit, namely as $L\to+\infty$.