{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:XUOMAVOLUZWIN62PRLCW5HBDNY","short_pith_number":"pith:XUOMAVOL","schema_version":"1.0","canonical_sha256":"bd1cc055cba66c86fb4f8ac56e9c236e0487c9c4dc064cbb7595e51261cdad9e","source":{"kind":"arxiv","id":"1012.5615","version":2},"attestation_state":"computed","paper":{"title":"Scaling Analysis in the Numerical Renormalization Group Study of the Sub-Ohmic Spin-Boson Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Ning-Hua Tong, Yan-Hua Hou","submitted_at":"2010-12-27T13:53:18Z","abstract_excerpt":"The spin-boson model has nontrivial quantum phase transitions in the sub-Ohmic regime. For the bath spectra exponent $0 \\leqslant s<1/2$, the bosonic numerical renormalization group (BNRG) study of the exponents $\\beta$ and $\\delta$ are hampered by the boson state truncation which leads to artificial interacting exponents instead of the correct Gaussian ones. In this paper, guided by a mean-field calculation, we study the order parameter function $m(\\tau=\\alpha-\\alpha_c, \\epsilon, \\Delta)$ using BNRG. Scaling analysis with respect to the boson state truncation $N_{b}$, the logarithmic discreti"},"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":"1012.5615","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.str-el","submitted_at":"2010-12-27T13:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"3cf2a7e981b53917981eaeb62ef115ecc89070335bc553122bd2715a709571cc","abstract_canon_sha256":"10bc7ee9ae3203c4a9ce9bda10312de8f314b95f82880257a28950d9f8d22d69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:00.895183Z","signature_b64":"xYUJCuSze6zCnwlsRtWPf6uOg41MmnEmQhouxOxOLOFJTTD0rVWNQRB9mgwEefXtVURRNsB/GIfKwlKIZvGYAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd1cc055cba66c86fb4f8ac56e9c236e0487c9c4dc064cbb7595e51261cdad9e","last_reissued_at":"2026-05-18T03:57:00.894364Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:00.894364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scaling Analysis in the Numerical Renormalization Group Study of the Sub-Ohmic Spin-Boson Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Ning-Hua Tong, Yan-Hua Hou","submitted_at":"2010-12-27T13:53:18Z","abstract_excerpt":"The spin-boson model has nontrivial quantum phase transitions in the sub-Ohmic regime. For the bath spectra exponent $0 \\leqslant s<1/2$, the bosonic numerical renormalization group (BNRG) study of the exponents $\\beta$ and $\\delta$ are hampered by the boson state truncation which leads to artificial interacting exponents instead of the correct Gaussian ones. In this paper, guided by a mean-field calculation, we study the order parameter function $m(\\tau=\\alpha-\\alpha_c, \\epsilon, \\Delta)$ using BNRG. Scaling analysis with respect to the boson state truncation $N_{b}$, the logarithmic discreti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.5615","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1012.5615","created_at":"2026-05-18T03:57:00.894478+00:00"},{"alias_kind":"arxiv_version","alias_value":"1012.5615v2","created_at":"2026-05-18T03:57:00.894478+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.5615","created_at":"2026-05-18T03:57:00.894478+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUOMAVOLUZWI","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUOMAVOLUZWIN62P","created_at":"2026-05-18T12:26:17.028572+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUOMAVOL","created_at":"2026-05-18T12:26:17.028572+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/XUOMAVOLUZWIN62PRLCW5HBDNY","json":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY.json","graph_json":"https://pith.science/api/pith-number/XUOMAVOLUZWIN62PRLCW5HBDNY/graph.json","events_json":"https://pith.science/api/pith-number/XUOMAVOLUZWIN62PRLCW5HBDNY/events.json","paper":"https://pith.science/paper/XUOMAVOL"},"agent_actions":{"view_html":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY","download_json":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY.json","view_paper":"https://pith.science/paper/XUOMAVOL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1012.5615&json=true","fetch_graph":"https://pith.science/api/pith-number/XUOMAVOLUZWIN62PRLCW5HBDNY/graph.json","fetch_events":"https://pith.science/api/pith-number/XUOMAVOLUZWIN62PRLCW5HBDNY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY/action/storage_attestation","attest_author":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY/action/author_attestation","sign_citation":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY/action/citation_signature","submit_replication":"https://pith.science/pith/XUOMAVOLUZWIN62PRLCW5HBDNY/action/replication_record"}},"created_at":"2026-05-18T03:57:00.894478+00:00","updated_at":"2026-05-18T03:57:00.894478+00:00"}