Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions
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| Format: | Preprint |
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2025
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| _version_ | 1866913748001751040 |
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| author | Braides, Andrea Caragiulo, Fabrizio |
| author_facet | Braides, Andrea Caragiulo, Fabrizio |
| contents | We consider large spin systems with short-range ferromagnetic interactions and long-range antiferromagnetic interactions subjected to periodic boundary conditions which have been proved by Giuliani, Lebowitz and Lieb to have minimizers that tend to alternate groups of $1$ and $-1$ of the same length $h^\star$. We consider states with energy of the same order as that of minimizers and show that they consist of a finite number of modulated phases of the same form as minimizers with some interfacial defects. The analysis is carried out using the notation of Gamma-convergence by exhibiting an interfacial energy that describes the minimal defect energy between different modulated phases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_16230 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions Braides, Andrea Caragiulo, Fabrizio Analysis of PDEs Mathematical Physics We consider large spin systems with short-range ferromagnetic interactions and long-range antiferromagnetic interactions subjected to periodic boundary conditions which have been proved by Giuliani, Lebowitz and Lieb to have minimizers that tend to alternate groups of $1$ and $-1$ of the same length $h^\star$. We consider states with energy of the same order as that of minimizers and show that they consist of a finite number of modulated phases of the same form as minimizers with some interfacial defects. The analysis is carried out using the notation of Gamma-convergence by exhibiting an interfacial energy that describes the minimal defect energy between different modulated phases. |
| title | Modulated phases in Ising systems with long-range antiferromagnetic and short-range ferromagnetic interactions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2503.16230 |