{"paper":{"title":"Irreducible Ginzburg-Landau fields in dimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DG","math.MP"],"primary_cat":"math-ph","authors_text":"\\'Akos Nagy","submitted_at":"2016-07-01T13:15:33Z","abstract_excerpt":"Ginzburg-Landau fields are the solutions of the Ginzburg-Landau equations which depend on two positive parameters, $\\alpha$ and $\\beta$. We give conditions on $\\alpha$ and $\\beta$ for the existence of irreducible solutions of these equations. Our results hold for arbitrary compact, oriented, Riemannian 2-manifolds (for example, bounded domains in $\\mathbb{R}^2$, spheres, tori, etc.) with de Gennes-Neumann boundary conditions. We also prove that, for each such manifold and all positive $\\alpha$ and $\\beta$, the Ginzburg-Landau free energy is a Palais-Smale function on the space of gauge equival"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00232","kind":"arxiv","version":4},"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"}