Preprint

Inserted: 10 jun 2026
Last Updated: 10 jun 2026

Year: 2026

Abstract:

We study a two-dimensional variational model for ferronematics — composite materials formed by dispersing magnetic nanoparticles into a liquid crystal matrix. The model features two coupled order parameters: a Landau-de Gennes Q-tensor for the liquid crystal component and a magnetisation vector field M, both of them governed by a Ginzburg-Landau-type energy. The energy, the largest part of which is carried by the Q-component, includes a singular coupling term favouring alignment between Q and M. In this article and in a companion paper, we analyse the asymptotic behaviour of (not necessarily minimizing) critical points as a small parameter ε tends to zero. In this paper, we prove that the (rescaled) energy density for the Q-component, concentrates, to leading order, on a finite number of singular points. Moreover, we prove energy estimates and compactness results that will be crucially used in 18 to determine the structure of the energy concentration set for the M- component as well as the relationship between the two singular sets.

Keywords: Rectifiable sets, Topological singularities, Allen-Cahn equation, Ginzburg-Landau functional, vectorial problems

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• GLAC-Part1-2026-05-27.pdf