2025/03/19 by Luca Briani, Briani, Luca, Marco Cicalese +3
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #High-pressure geophysics and materials #Magnetic Properties of Alloys #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2503.15151
openalex publication_date 2025/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the formation of singularities in a baby Skyrme type energy model, which describes magnetic solitons in two-dimensional ferromagnetic systems. In presence of a diverging anisotropy term, which enforces a preferred background state of the magnetization, we establish a weak compactness of its topological charge density, which converges to an atomic measure with quantized weights. We characterize the Γ-limit of the energies as the total variation of this measure. In the case of lattice type energies, we first need to carefully define a notion of discrete topological charge for \mathbbS2-valued maps. We then prove a corresponding compactness and Γ-convergence result, thereby bridging the discrete and continuum theories.