{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:P4XVAHFQO47JVOGJGPH7MAPMBG","short_pith_number":"pith:P4XVAHFQ","canonical_record":{"source":{"id":"1511.03031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-11-10T09:27:55Z","cross_cats_sorted":[],"title_canon_sha256":"9808f5b415f41ad9ad4166b8eddb4449ff927a6b5d5898a76cdbe3f24ca2d920","abstract_canon_sha256":"928cc547e95304aa1f554b42857a5ee4df24948eb4e5c332d9d972d5b571d744"},"schema_version":"1.0"},"canonical_sha256":"7f2f501cb0773e9ab8c933cff601ec09ac77bd226335abacb03f541ba1b18103","source":{"kind":"arxiv","id":"1511.03031","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03031","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03031v2","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03031","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"pith_short_12","alias_value":"P4XVAHFQO47J","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P4XVAHFQO47JVOGJ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P4XVAHFQ","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:P4XVAHFQO47JVOGJGPH7MAPMBG","target":"record","payload":{"canonical_record":{"source":{"id":"1511.03031","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-11-10T09:27:55Z","cross_cats_sorted":[],"title_canon_sha256":"9808f5b415f41ad9ad4166b8eddb4449ff927a6b5d5898a76cdbe3f24ca2d920","abstract_canon_sha256":"928cc547e95304aa1f554b42857a5ee4df24948eb4e5c332d9d972d5b571d744"},"schema_version":"1.0"},"canonical_sha256":"7f2f501cb0773e9ab8c933cff601ec09ac77bd226335abacb03f541ba1b18103","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:14.762933Z","signature_b64":"eGDhjAQjdX+dMGOMcu2mpno9HoBo53i/m+m4wNJiL+Hh2B/clDBEY3FWPIZ246rHozYmSAoda9Pmlv1ydztkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f2f501cb0773e9ab8c933cff601ec09ac77bd226335abacb03f541ba1b18103","last_reissued_at":"2026-05-18T01:27:14.762296Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:14.762296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.03031","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTJimHorsaST0/pxDzQh6sNDzX70Xgre8+hJMHn/IvSNWaHI3JOw2lzvxWRoGk7/VEvDKLh42S0utJ0R4WUbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:28:23.309879Z"},"content_sha256":"cd8487300a19b5eab0e4ef95d8a9fe3e85e5d6320a8927c54db0124df609e20b","schema_version":"1.0","event_id":"sha256:cd8487300a19b5eab0e4ef95d8a9fe3e85e5d6320a8927c54db0124df609e20b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:P4XVAHFQO47JVOGJGPH7MAPMBG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A brief account of the Ising and Ising-like models: Mean-field, effective-field and exact results","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jozef Strecka, Michal Jascur","submitted_at":"2015-11-10T09:27:55Z","abstract_excerpt":"The article provides a tutorial review on how to treat Ising models within mean-field (MF), effective-field (EF) and exact methods. MF solutions of the spin-1 Blume-Capel (BC) model and the mixed-spin Ising model demonstrate a change of continuous phase transitions to discontinuous ones at a tricritical point. A quantum phase transition of the spin-S Ising model driven by a transverse field is explored within MF method. EF theory is elaborated within a single- and two-spin cluster approach to demonstrate an efficiency of this approximate method. The long-standing problem of this method concern"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03031","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:27:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0AWIlaYoCvv4fF8i2IsE5GIBgMjIFlwopjaLW7RaKaNf2rOb/z1PhwvQJ+bHNzeqJxJV1gjLmD5Het9llj13Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T19:28:23.310222Z"},"content_sha256":"953eb1c4938fa244c9b3623982a29a3074ae48f6c94dcff70b2f8bb32eaf09f0","schema_version":"1.0","event_id":"sha256:953eb1c4938fa244c9b3623982a29a3074ae48f6c94dcff70b2f8bb32eaf09f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P4XVAHFQO47JVOGJGPH7MAPMBG/bundle.json","state_url":"https://pith.science/pith/P4XVAHFQO47JVOGJGPH7MAPMBG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P4XVAHFQO47JVOGJGPH7MAPMBG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-22T19:28:23Z","links":{"resolver":"https://pith.science/pith/P4XVAHFQO47JVOGJGPH7MAPMBG","bundle":"https://pith.science/pith/P4XVAHFQO47JVOGJGPH7MAPMBG/bundle.json","state":"https://pith.science/pith/P4XVAHFQO47JVOGJGPH7MAPMBG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P4XVAHFQO47JVOGJGPH7MAPMBG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:P4XVAHFQO47JVOGJGPH7MAPMBG","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":"928cc547e95304aa1f554b42857a5ee4df24948eb4e5c332d9d972d5b571d744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-11-10T09:27:55Z","title_canon_sha256":"9808f5b415f41ad9ad4166b8eddb4449ff927a6b5d5898a76cdbe3f24ca2d920"},"schema_version":"1.0","source":{"id":"1511.03031","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03031","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03031v2","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03031","created_at":"2026-05-18T01:27:14Z"},{"alias_kind":"pith_short_12","alias_value":"P4XVAHFQO47J","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"P4XVAHFQO47JVOGJ","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"P4XVAHFQ","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:953eb1c4938fa244c9b3623982a29a3074ae48f6c94dcff70b2f8bb32eaf09f0","target":"graph","created_at":"2026-05-18T01:27:14Z","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":"The article provides a tutorial review on how to treat Ising models within mean-field (MF), effective-field (EF) and exact methods. MF solutions of the spin-1 Blume-Capel (BC) model and the mixed-spin Ising model demonstrate a change of continuous phase transitions to discontinuous ones at a tricritical point. A quantum phase transition of the spin-S Ising model driven by a transverse field is explored within MF method. EF theory is elaborated within a single- and two-spin cluster approach to demonstrate an efficiency of this approximate method. The long-standing problem of this method concern","authors_text":"Jozef Strecka, Michal Jascur","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-11-10T09:27:55Z","title":"A brief account of the Ising and Ising-like models: Mean-field, effective-field and exact results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03031","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:cd8487300a19b5eab0e4ef95d8a9fe3e85e5d6320a8927c54db0124df609e20b","target":"record","created_at":"2026-05-18T01:27:14Z","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":"928cc547e95304aa1f554b42857a5ee4df24948eb4e5c332d9d972d5b571d744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-11-10T09:27:55Z","title_canon_sha256":"9808f5b415f41ad9ad4166b8eddb4449ff927a6b5d5898a76cdbe3f24ca2d920"},"schema_version":"1.0","source":{"id":"1511.03031","kind":"arxiv","version":2}},"canonical_sha256":"7f2f501cb0773e9ab8c933cff601ec09ac77bd226335abacb03f541ba1b18103","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f2f501cb0773e9ab8c933cff601ec09ac77bd226335abacb03f541ba1b18103","first_computed_at":"2026-05-18T01:27:14.762296Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:14.762296Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eGDhjAQjdX+dMGOMcu2mpno9HoBo53i/m+m4wNJiL+Hh2B/clDBEY3FWPIZ246rHozYmSAoda9Pmlv1ydztkBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:14.762933Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03031","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd8487300a19b5eab0e4ef95d8a9fe3e85e5d6320a8927c54db0124df609e20b","sha256:953eb1c4938fa244c9b3623982a29a3074ae48f6c94dcff70b2f8bb32eaf09f0"],"state_sha256":"ee662f52bf95d4f8e506014d6ba0dafffc74499b2c5b06c3bc93ca3c7d94554b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lD6xjQNF3aczt0z9S/Q+AmQDcvkJR3TJM/a8fazgXroUs6hNdHdgeFmaYiqQbZruQ+dzL9xpvtUQ6wRIiLFfBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T19:28:23.312244Z","bundle_sha256":"7b8980bbcda875e64808e84924a1cd4d68e16649430c13aa3f948f62b7187f58"}}