{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HF5IJPE76VEKLE2BI6XJPO2M5K","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":"f3e4db120dd5b0015fcee328402b1f559a35575e1273268ed9e46ab01b0dec5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-05-31T04:46:54Z","title_canon_sha256":"33dcccda4c4194db2c0b8a158bf4cc3bbd8440d751fd5939164aacaa375049a5"},"schema_version":"1.0","source":{"id":"1605.09496","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09496","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09496v3","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09496","created_at":"2026-05-18T00:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"HF5IJPE76VEK","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"HF5IJPE76VEKLE2B","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"HF5IJPE7","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:e6b28e0f77ccd79b4af700f80b11ed6630b83c4949781c1245a5135d95448fd2","target":"graph","created_at":"2026-05-18T00:34:15Z","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 investigate the universality class of the finite-temperature phase transition of the two-dimensional Ising model with the algebraically decaying ferromagnetic long-range interaction, $J_{ij} = |\\vec{r}_i -\\vec{r}_j|^{-(d+\\sigma)}$, where $d$ (=2) is the dimension of the system and $\\sigma$ the decay exponent, by means of the order-$N$ cluster-algorithm Monte Carlo method. In particular, we focus on the upper and lower critical decay exponents, the boundaries between the mean-field-universality, intermediate, and short-range-universality regimes. At the critical decay exponents, it is found ","authors_text":"Hidemaro Suwa, Synge Todo, Toshiki Horita","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-05-31T04:46:54Z","title":"Upper and Lower Critical Decay Exponents of Ising Ferromagnets with Long-range Interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09496","kind":"arxiv","version":3},"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":"sha256:5e523808a576782bb290a7b39896c0b943b5d0b375528b6433ddd47e64c5a6bd","target":"record","created_at":"2026-05-18T00:34:15Z","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":"f3e4db120dd5b0015fcee328402b1f559a35575e1273268ed9e46ab01b0dec5f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-05-31T04:46:54Z","title_canon_sha256":"33dcccda4c4194db2c0b8a158bf4cc3bbd8440d751fd5939164aacaa375049a5"},"schema_version":"1.0","source":{"id":"1605.09496","kind":"arxiv","version":3}},"canonical_sha256":"397a84bc9ff548a5934147ae97bb4ceab7f9dc2e9e565dd82d34d3934352a38d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"397a84bc9ff548a5934147ae97bb4ceab7f9dc2e9e565dd82d34d3934352a38d","first_computed_at":"2026-05-18T00:34:15.910738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:15.910738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aTTbBD90N6CTHDPCdq4juY7BhMs8DlvQb2st+r+JrS2Sf1OqdtQqhRGQAiCqTQCGRGKG6o5WFZXX1D9wWy7SCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:15.911204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09496","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5e523808a576782bb290a7b39896c0b943b5d0b375528b6433ddd47e64c5a6bd","sha256:e6b28e0f77ccd79b4af700f80b11ed6630b83c4949781c1245a5135d95448fd2"],"state_sha256":"b11fc85e0a694e19da21d35a22d80148673221f88425d62bec32da15adc13a19"}