{"paper":{"title":"Asymptotic Scaling in the Two-Dimensional $O(3)$ $\\sigma$-Model at Correlation Length $10^5$","license":"","headline":"","cross_cats":[],"primary_cat":"hep-lat","authors_text":"Alan D. Sokal, Andrea Pelissetto, Robert G. Edwards, Sergio Caracciolo","submitted_at":"1994-11-07T23:52:48Z","abstract_excerpt":"We carry out a high-precision Monte Carlo simulation of the two-dimensional $O(3)$-invariant $\\sigma$-model at correlation lengths $\\xi$ up to $\\sim 10^5$. Our work employs a new and powerful method for extrapolating finite-volume Monte Carlo data to infinite volume, based on finite-size-scaling theory. We discuss carefully the systematic and statistical errors in this extrapolation. We then compare the extrapolated data to the renormalization-group predictions. The deviation from asymptotic scaling, which is $\\approx 25\\%$ at $\\xi \\sim 10^2$, decreases to $\\approx 4\\%$ at $\\xi \\sim 10^5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9411009","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-lat/9411009/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}