{"paper":{"title":"\"Zero\" temperature stochastic 3D Ising model and dimer covering fluctuations: a first step towards interface mean curvature motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Fabio Lucio Toninelli, Fabio Martinelli, Francois Simenhaus, Pietro Caputo","submitted_at":"2010-07-21T09:48:06Z","abstract_excerpt":"We consider the Glauber dynamics for the Ising model with \"+\" boundary conditions, at zero temperature or at temperature which goes to zero with the system size (hence the quotation marks in the title). In dimension d=3 we prove that an initial domain of linear size L of \"-\" spins disappears within a time \\tau_+ which is at most L^2(\\log L)^c and at least L^2/(c\\log L), for some c>0. The proof of the upper bound proceeds via comparison with an auxiliary dynamics which mimics the motion by mean curvature that is expected to describe, on large time-scales, the evolution of the interface between "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.3599","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"}