{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:4Z23FGKZMOW5RYEFDGA22GJJEY","short_pith_number":"pith:4Z23FGKZ","schema_version":"1.0","canonical_sha256":"e675b2995963add8e0851981ad1929263aa64629c6e49d9724ba5fdbba4a1707","source":{"kind":"arxiv","id":"hep-lat/9411009","version":2},"attestation_state":"computed","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 $\\xi \\sim 10^5$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"hep-lat/9411009","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"hep-lat","submitted_at":"1994-11-07T23:52:48Z","cross_cats_sorted":[],"title_canon_sha256":"75f6f59d0bd257317081465abad9cdc889dfa33bf11e6b1c11cd7bc004b7b459","abstract_canon_sha256":"4d96a587d75726b3519293df9c0b5cfed320d0babb64c2cbb1bd64b27e59a058"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:57:06.670838Z","signature_b64":"3HMU2MU1c7/23Kkc0JoNLGSwq5Plf4W+Q7m/Ppua5MLRTA5McatFfZys24rdoAdqXKXuj3+8BooOzF4Q+nM2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e675b2995963add8e0851981ad1929263aa64629c6e49d9724ba5fdbba4a1707","last_reissued_at":"2026-07-04T15:57:06.670469Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:57:06.670469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/9411009","created_at":"2026-07-04T15:57:06.670530+00:00"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/9411009v2","created_at":"2026-07-04T15:57:06.670530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/9411009","created_at":"2026-07-04T15:57:06.670530+00:00"},{"alias_kind":"pith_short_12","alias_value":"4Z23FGKZMOW5","created_at":"2026-07-04T15:57:06.670530+00:00"},{"alias_kind":"pith_short_16","alias_value":"4Z23FGKZMOW5RYEF","created_at":"2026-07-04T15:57:06.670530+00:00"},{"alias_kind":"pith_short_8","alias_value":"4Z23FGKZ","created_at":"2026-07-04T15:57:06.670530+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2502.05716","citing_title":"Qubit Regularization of Quantum Field Theories","ref_index":6,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY","json":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY.json","graph_json":"https://pith.science/api/pith-number/4Z23FGKZMOW5RYEFDGA22GJJEY/graph.json","events_json":"https://pith.science/api/pith-number/4Z23FGKZMOW5RYEFDGA22GJJEY/events.json","paper":"https://pith.science/paper/4Z23FGKZ"},"agent_actions":{"view_html":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY","download_json":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY.json","view_paper":"https://pith.science/paper/4Z23FGKZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=hep-lat/9411009&json=true","fetch_graph":"https://pith.science/api/pith-number/4Z23FGKZMOW5RYEFDGA22GJJEY/graph.json","fetch_events":"https://pith.science/api/pith-number/4Z23FGKZMOW5RYEFDGA22GJJEY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY/action/storage_attestation","attest_author":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY/action/author_attestation","sign_citation":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY/action/citation_signature","submit_replication":"https://pith.science/pith/4Z23FGKZMOW5RYEFDGA22GJJEY/action/replication_record"}},"created_at":"2026-07-04T15:57:06.670530+00:00","updated_at":"2026-07-04T15:57:06.670530+00:00"}