{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:ZWCQFCVD6ZCCJSVPGZUMOCATSD","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a4793fe5d00823cb4564dab167f0adc4818a6cc6483725223512beb5fc106280","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"1996-04-18T17:21:30Z","title_canon_sha256":"7e6733f5159aff68a6a03c179641c01c852260d28c782631e1538e2d00c4dc28"},"schema_version":"1.0","source":{"id":"hep-lat/9604015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-lat/9604015","created_at":"2026-05-18T04:17:45Z"},{"alias_kind":"arxiv_version","alias_value":"hep-lat/9604015v1","created_at":"2026-05-18T04:17:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-lat/9604015","created_at":"2026-05-18T04:17:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZWCQFCVD6ZCC","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"ZWCQFCVD6ZCCJSVP","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"ZWCQFCVD","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:2948e9cb17c40dec067b55bbc3a7f9f50aca302f0c40705c1c8be213f6dabb54","target":"graph","created_at":"2026-05-18T04:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an $XY$ model into the target model, and we study its mathematical properties for a variety of nonlinear $\\sigma$-models. We then apply the method to the two-dimensional $O(N)$-symmetric nonlinear $\\sigma$-models (also called $N$-vector models) with $N=3,4,8$ and study its dynamic critical behavior. Using lattices up to $256 \\times 256$, we find dynamic critical exponents $z_{int,{\\cal M}^2} \\approx 0.70 \\pm 0.08$, $0.60 \\pm 0.07$, $0.52 \\pm 0.10$ for $N=3,4,8$, respectively (subjective 68\\% confidenc","authors_text":"Alan D. Sokal (New York University), Andrea Pelissetto, Tereza Mendes","cross_cats":[],"headline":"","license":"","primary_cat":"hep-lat","submitted_at":"1996-04-18T17:21:30Z","title":"Multi-Grid Monte Carlo via $XY$ Embedding I. General Theory and Two-Dimensional $O(N)$-Symmetric Nonlinear $\\sigma$-Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-lat/9604015","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2ced9132a04629faeae29a14e3e1bcbbdff73ab6230d8e112c2d4847e9d09025","target":"record","created_at":"2026-05-18T04:17:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a4793fe5d00823cb4564dab167f0adc4818a6cc6483725223512beb5fc106280","cross_cats_sorted":[],"license":"","primary_cat":"hep-lat","submitted_at":"1996-04-18T17:21:30Z","title_canon_sha256":"7e6733f5159aff68a6a03c179641c01c852260d28c782631e1538e2d00c4dc28"},"schema_version":"1.0","source":{"id":"hep-lat/9604015","kind":"arxiv","version":1}},"canonical_sha256":"cd85028aa3f64424caaf3668c7081390d03800dd22f2f5c2a30dba2432ae937d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd85028aa3f64424caaf3668c7081390d03800dd22f2f5c2a30dba2432ae937d","first_computed_at":"2026-05-18T04:17:45.908575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:17:45.908575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ycz16A8aPRUDm+sUwBqr5Zpk0cz+L8oIXJAaIlRUAHm2ka2mPogLO2KJxc6eDcWPVfRreBPMuKcgpXeQud2LCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:17:45.909100Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-lat/9604015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ced9132a04629faeae29a14e3e1bcbbdff73ab6230d8e112c2d4847e9d09025","sha256:2948e9cb17c40dec067b55bbc3a7f9f50aca302f0c40705c1c8be213f6dabb54"],"state_sha256":"130aea127c9fc89228c29f82668cfc7961ff01a322310bcccd4f977c99b2297e"}