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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.15151 |
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| _version_ | 1866915204925751296 |
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| author | Briani, Luca Cicalese, Marco Kreutz, Leonard |
| author_facet | Briani, Luca Cicalese, Marco Kreutz, Leonard |
| contents | 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 $\mathbb{S}^2$-valued maps. We then prove a corresponding compactness and $Γ$-convergence result, thereby bridging the discrete and continuum theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Energy concentration in a two-dimensional magnetic skyrmion model: variational analysis of lattice and continuum theories Briani, Luca Cicalese, Marco Kreutz, Leonard Analysis of PDEs 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 $\mathbb{S}^2$-valued maps. We then prove a corresponding compactness and $Γ$-convergence result, thereby bridging the discrete and continuum theories. |
| title | Energy concentration in a two-dimensional magnetic skyrmion model: variational analysis of lattice and continuum theories |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.15151 |