{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:JBRKUEKF7CM7AE7BUZP5N3XHBE","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":"e1d493df11bfba1cfcbb6a806c0eafa5158aceb28fb19ab2821eaf3f3857e323","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-27T11:07:06Z","title_canon_sha256":"e4795694aa508523ec2f11a2500cdcd3a7266381b302ac625cfb89329fcc057e"},"schema_version":"1.0","source":{"id":"1401.6805","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.6805","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1401.6805v2","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.6805","created_at":"2026-05-18T02:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"JBRKUEKF7CM7","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"JBRKUEKF7CM7AE7B","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"JBRKUEKF","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:ec6dbdcf8b32eeef1d67cec28f587a8f5f009a314c983e9247c65bb68c69635f","target":"graph","created_at":"2026-05-18T02:49:53Z","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 perform a numerical study of the long range (LR) ferromagnetic Ising model with power law decaying interactions ($J \\propto r^{-d-\\sigma}$) both on a one-dimensional chain ($d=1$) and on a square lattice ($d=2$). We use advanced cluster algorithms to avoid the critical slowing down. We first check the validity of the relation connecting the critical behavior of the LR model with parameters $(d,\\sigma)$ to that of a short range (SR) model in an equivalent dimension $D$. We then study the critical behavior of the $d=2$ LR model close to the lower critical $\\sigma$, uncovering that the spatial","authors_text":"Federico Ricci-Tersenghi, Giorgio Parisi, Maria Chiara Angelini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-27T11:07:06Z","title":"Relations between Short Range and Long Range Ising models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.6805","kind":"arxiv","version":2},"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":"sha256:0e85db752e466747e866e39cabad7c6c01e3c52b35af781708e7ba0845e671dd","target":"record","created_at":"2026-05-18T02:49:53Z","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":"e1d493df11bfba1cfcbb6a806c0eafa5158aceb28fb19ab2821eaf3f3857e323","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-01-27T11:07:06Z","title_canon_sha256":"e4795694aa508523ec2f11a2500cdcd3a7266381b302ac625cfb89329fcc057e"},"schema_version":"1.0","source":{"id":"1401.6805","kind":"arxiv","version":2}},"canonical_sha256":"4862aa1145f899f013e1a65fd6eee7091138dd91a4f198ed39b3bfd3f8ce19fc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4862aa1145f899f013e1a65fd6eee7091138dd91a4f198ed39b3bfd3f8ce19fc","first_computed_at":"2026-05-18T02:49:53.690067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:53.690067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3RlteK56/cx8yj75GckyqMATTBjaLy0KXzUHBd84WVoQbWoHDLNGfeqlnVLsrxrY48l+4ZWL7z77XFqrao7LCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:53.690496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.6805","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e85db752e466747e866e39cabad7c6c01e3c52b35af781708e7ba0845e671dd","sha256:ec6dbdcf8b32eeef1d67cec28f587a8f5f009a314c983e9247c65bb68c69635f"],"state_sha256":"b35be8c5f7cffde77e9619571410427147443eba12aba08cda8f6410d027e296"}