{"paper":{"title":"Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"David S. Dean, Peter Grassberger, Satya N. Majumdar","submitted_at":"2000-04-28T12:35:05Z","abstract_excerpt":"We study the zero temperature coarsening dynamics in an Ising chain in presence of a dynamically induced field that favors locally the `-' phase compared to the `+' phase. At late times, while the `+' domains still coarsen as $t^{1/2}$, the `-' domains coarsen slightly faster as $t^{1/2}\\log (t)$. As a result, at late times, the magnetization decays slowly as, $m(t)=-1 +{\\rm const.}/{\\log (t)}$. We establish this behavior both analytically within an independent interval approximation (IIA) and numerically. In the zero volume fraction limit of the `+' phase, we argue that the IIA becomes asympt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0004486","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"}