{"paper":{"title":"Droplet minimizers for the Gates-Lebowitz-Penrose free energy functional","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"E. A. Carlen, J. L. Lebowitz, M. C. Carvalho, R. Esposito, R. Marra","submitted_at":"2009-05-21T23:37:48Z","abstract_excerpt":"We study the structure of the constrained minimizers of the Gates-Lebowitz-Penrose free-energy functional ${\\mathcal F}_{\\rm GLP}(m)$, non-local functional of a density field $m(x)$, $x\\in {\\mathcal T}_L$, a $d$-dimensional torus of side length $L$. At low temperatures, ${\\mathcal F}_{\\rm GLP}$ is not convex, and has two distinct global minimizers, corresponding to two equilibrium states. Here we constrain the average density $L^{-d}\\int_{{\\cal T}_L}m(x)\\dd x$ to be a fixed value $n$ between the densities in the two equilibrium states, but close to the low density equilibrium value. In this ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3583","kind":"arxiv","version":1},"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"}