{"paper":{"title":"Domain formation in magnetic polymer composites: an approach via stochastic homogenization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"M. Cicalese, M. Ruf, R. Alicandro","submitted_at":"2014-11-17T13:08:49Z","abstract_excerpt":"We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter $\\varepsilon$ and the magnets as classical $\\pm 1$ spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of $\\Gamma$-convergence that, up to subsequences, the (continuum) $\\Gamma$-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4463","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}