{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:ASFYABEEWK2PNXPY5J7NHJFU3T","short_pith_number":"pith:ASFYABEE","schema_version":"1.0","canonical_sha256":"048b800484b2b4f6ddf8ea7ed3a4b4dcf5d3b67af77b5027d691e3038a93b6be","source":{"kind":"arxiv","id":"1605.04546","version":1},"attestation_state":"computed","paper":{"title":"Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.FA","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Abdessatar Barhoumi, Abdessatar Souissi, Farrukh Mukhamedov","submitted_at":"2016-05-15T13:30:07Z","abstract_excerpt":"The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing inte"},"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":"1605.04546","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-05-15T13:30:07Z","cross_cats_sorted":["cond-mat.stat-mech","math.FA","math.MP","math.OA","quant-ph"],"title_canon_sha256":"67f3150705902e5cc704ebbe8a3201b14c02070ae52529f585cd4ef56548c1c8","abstract_canon_sha256":"7390d29a063845af3c8bdf333437e8073f6ba9b7b7c96198de601c16725b1c04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:46.872155Z","signature_b64":"QOTmcINsMLmpgYPfIKmYIR/xzf82Vkb6gA207BwtYApxyghzOFIzuD2BrKiRCffy49jtgZZovMhZ4AseJD6xCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"048b800484b2b4f6ddf8ea7ed3a4b4dcf5d3b67af77b5027d691e3038a93b6be","last_reissued_at":"2026-05-18T01:14:46.871461Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:46.871461Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase transitions for Quantum Markov Chains associated with Ising type models on a Cayley tree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.FA","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Abdessatar Barhoumi, Abdessatar Souissi, Farrukh Mukhamedov","submitted_at":"2016-05-15T13:30:07Z","abstract_excerpt":"The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04546","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.04546","created_at":"2026-05-18T01:14:46.871584+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.04546v1","created_at":"2026-05-18T01:14:46.871584+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04546","created_at":"2026-05-18T01:14:46.871584+00:00"},{"alias_kind":"pith_short_12","alias_value":"ASFYABEEWK2P","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_16","alias_value":"ASFYABEEWK2PNXPY","created_at":"2026-05-18T12:30:07.202191+00:00"},{"alias_kind":"pith_short_8","alias_value":"ASFYABEE","created_at":"2026-05-18T12:30:07.202191+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T","json":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T.json","graph_json":"https://pith.science/api/pith-number/ASFYABEEWK2PNXPY5J7NHJFU3T/graph.json","events_json":"https://pith.science/api/pith-number/ASFYABEEWK2PNXPY5J7NHJFU3T/events.json","paper":"https://pith.science/paper/ASFYABEE"},"agent_actions":{"view_html":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T","download_json":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T.json","view_paper":"https://pith.science/paper/ASFYABEE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.04546&json=true","fetch_graph":"https://pith.science/api/pith-number/ASFYABEEWK2PNXPY5J7NHJFU3T/graph.json","fetch_events":"https://pith.science/api/pith-number/ASFYABEEWK2PNXPY5J7NHJFU3T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T/action/storage_attestation","attest_author":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T/action/author_attestation","sign_citation":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T/action/citation_signature","submit_replication":"https://pith.science/pith/ASFYABEEWK2PNXPY5J7NHJFU3T/action/replication_record"}},"created_at":"2026-05-18T01:14:46.871584+00:00","updated_at":"2026-05-18T01:14:46.871584+00:00"}