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One-dimensionality of the minimizers in the large volume limit for a diffuse interface attractive/repulsive model in general dimension
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One-dimensionality of the minimizers in the large volume limit for a diffuse interface attractive/repulsive model in general dimension
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Paper
One-dimensionality of the minimizers in the large volume limit for a diffuse interface attractive/repulsive model in general dimension
2021
Overview
In this paper we consider the diffuse interface generalized antiferromagnetic model with local/nonlocal attractive/repulsive terms in competition studied in Daneri-Kerschbaum-Runa arXiv:1907.06419. The parameters of the model are denoted by \\(\\) and \\(\\): the parameter \\(\\) represents the relative strength of the local term with respect to the nonlocal one, while the parameter \\(\\) 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 \\(d1\\) and for small but positive \\(\\) and \\(\\) (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+ınfty\\).
Publisher
Cornell University Library, arXiv.org
Subject
