{"paper":{"title":"Zero-temperature 2D Ising model and anisotropic curve-shortening flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"F. L. Toninelli, F. Simenhaus, H. Lacoin","submitted_at":"2011-12-14T10:36:36Z","abstract_excerpt":"Let $\\DD$ be a simply connected, smooth enough domain of $\\bbR^2$. For $L>0$ consider the continuous time, zero-temperature heat bath dynamics for the nearest-neighbor Ising model on $\\mathbb Z^2$ with initial condition such that $\\sigma_x=-1$ if $x\\in L\\DD$ and $\\sigma_x=+1$ otherwise. It is conjectured \\cite{cf:Spohn} that, in the diffusive limit where space is rescaled by $L$, time by $L^2$ and $L\\to\\infty$, the boundary of the droplet of \"$-$\" spins follows a \\emph{deterministic} anisotropic curve-shortening flow, where the normal velocity at a point of its boundary is given by the local c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3160","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"}