{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KOUA46G3N63N6IKDIIJMBOQSAB","short_pith_number":"pith:KOUA46G3","schema_version":"1.0","canonical_sha256":"53a80e78db6fb6df21434212c0ba12006667588f9cee841529b3f8cff655f31b","source":{"kind":"arxiv","id":"1712.03699","version":2},"attestation_state":"computed","paper":{"title":"A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Ron Peled, Yinon Spinka","submitted_at":"2017-12-11T09:53:40Z","abstract_excerpt":"We give a general condition for a discrete spin system with nearest-neighbor interactions on the $\\mathbb{Z}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order is entropically driven. As a main example we consider the antiferromagnetic $q$-state Potts model and rigorously prove the existence of a broken sub-lattice symmetry phase at low temperature and high dimension -- a new result for $q\\ge 4$. As further examples, we prove the existence of an ordered phase in a clock model with hard constraints and extend the kn"},"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":"1712.03699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-12-11T09:53:40Z","cross_cats_sorted":["hep-lat","math-ph","math.MP","math.PR"],"title_canon_sha256":"e73d5ab1fffbf15ade6c85103c764e27e8446c117f24462f19c812d54be5293d","abstract_canon_sha256":"c2665c57cf284028355432b259e6c5d08849c3fccb10f2e004fc77768040ef8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:59.919211Z","signature_b64":"SxyZBzdEF1DmFodJ87IVLDlyy4pGXueSf4MV+dI1cOk4RKFh4PA1g3A1iH0HGBE0p31RCTFcLE2H++6Fhm23DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"53a80e78db6fb6df21434212c0ba12006667588f9cee841529b3f8cff655f31b","last_reissued_at":"2026-05-18T00:26:59.918531Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:59.918531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A condition for long-range order in discrete spin systems with application to the antiferromagnetic Potts model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Ron Peled, Yinon Spinka","submitted_at":"2017-12-11T09:53:40Z","abstract_excerpt":"We give a general condition for a discrete spin system with nearest-neighbor interactions on the $\\mathbb{Z}^d$ lattice to exhibit long-range order. The condition is applicable to systems with residual entropy in which the long-range order is entropically driven. As a main example we consider the antiferromagnetic $q$-state Potts model and rigorously prove the existence of a broken sub-lattice symmetry phase at low temperature and high dimension -- a new result for $q\\ge 4$. As further examples, we prove the existence of an ordered phase in a clock model with hard constraints and extend the kn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.03699","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":"1712.03699","created_at":"2026-05-18T00:26:59.918630+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.03699v2","created_at":"2026-05-18T00:26:59.918630+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.03699","created_at":"2026-05-18T00:26:59.918630+00:00"},{"alias_kind":"pith_short_12","alias_value":"KOUA46G3N63N","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KOUA46G3N63N6IKD","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KOUA46G3","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2010.03177","citing_title":"Long-range order in discrete spin systems","ref_index":70,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB","json":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB.json","graph_json":"https://pith.science/api/pith-number/KOUA46G3N63N6IKDIIJMBOQSAB/graph.json","events_json":"https://pith.science/api/pith-number/KOUA46G3N63N6IKDIIJMBOQSAB/events.json","paper":"https://pith.science/paper/KOUA46G3"},"agent_actions":{"view_html":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB","download_json":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB.json","view_paper":"https://pith.science/paper/KOUA46G3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.03699&json=true","fetch_graph":"https://pith.science/api/pith-number/KOUA46G3N63N6IKDIIJMBOQSAB/graph.json","fetch_events":"https://pith.science/api/pith-number/KOUA46G3N63N6IKDIIJMBOQSAB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB/action/storage_attestation","attest_author":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB/action/author_attestation","sign_citation":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB/action/citation_signature","submit_replication":"https://pith.science/pith/KOUA46G3N63N6IKDIIJMBOQSAB/action/replication_record"}},"created_at":"2026-05-18T00:26:59.918630+00:00","updated_at":"2026-05-18T00:26:59.918630+00:00"}