{"paper":{"title":"Nucleation and growth for the Ising model in $d$ dimensions at very low temperatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francesco Manzo, Rapha\\\"el Cerf","submitted_at":"2011-02-08T22:20:21Z","abstract_excerpt":"This work extends to dimension $d\\geq3$ the main result of Dehghanpour and Schonmann. We consider the stochastic Ising model on ${\\mathbb{Z}}^d$ evolving with the Metropolis dynamics under a fixed small positive magnetic field $h$ starting from the minus phase. When the inverse temperature $\\beta$ goes to $\\infty$, the relaxation time of the system, defined as the time when the plus phase has invaded the origin, behaves like $\\exp({{\\beta}{\\kappa}_d})$. The value $\\kappa_d$ is equal to \\[{\\kappa}_d=\\frac{1}{d+1}({\\Gamma}_1+\\cdots+{\\Gamma}_d),\\] where ${\\Gamma}_i$ is the energy of the $i$-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1741","kind":"arxiv","version":3},"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"}