Preprint

Inserted: 10 jun 2026
Last Updated: 10 jun 2026

Year: 2026
Notes:

In this paper, we continue our study of 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 includes a singular coupling term favouring alignment between Q and M. We analyse the asymptotic behaviour of (not necessarily minimizing) critical points as a small parameter ε tends to zero. While in a companion paper we showed that the (rescaled) energy density for the Q-component concentrates, to leading order, on a finite number of singular points, in this paper we prove the energy density for the M-component concentrates along a one-dimensional rectifiable set. Moreover, we prove that the curvature of the singular set for the M-component (technically, the first variation of the associated varifold) is concentrated on a finite number of points, i.e. the singular set for the Q-component. Crucial to our arguments will be the energy estimates and compactness results proved in a companion paper.

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

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• GLAC-Part2-2026-05-27.pdf