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It is pointed out that the percolation transition of the Fortuin-Kasteleyn cluster for the spin glass model is related to a dynamical transition for the freezing of spins. The present results are obtained as locations of points on the so-called Nishimori line, which is a special line in the phase diagram. We obtain TFK = 2 / ln [z / (z - 2)] and pFK = z / [2 (z - 1)] for the Bethe lattice, TFK -> infinity and pFK -> 1 / 2 for the infini"},"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":"1004.0654","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2010-04-05T16:19:39Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"fb5f7f9875c10890ba6b452481ada895907e5abf8972b29a3386471f767bbca9","abstract_canon_sha256":"613eb75e7df0d461a954b2ed305f61ffa599e33671d6a5c239fdcc379408af19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:17.607161Z","signature_b64":"rYdaCIBPxfalcLMWJfZnHsw6slcxdLEs8W28IHGbzTsNU1RJU7A4JyKDnwJQkEoicpES9I/KirqUp6fA2udcBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85fd75e73e79a11cf9b71b0fc6f331d5fd07d9ce4273a1bf8859e1d17e47cc20","last_reissued_at":"2026-05-18T02:24:17.606441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:17.606441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conjectured Exact Percolation Thresholds of the Fortuin-Kasteleyn Cluster for the +-J Ising Spin Glass Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Chiaki Yamaguchi","submitted_at":"2010-04-05T16:19:39Z","abstract_excerpt":"The conjectured exact percolation thresholds of the Fortuin-Kasteleyn cluster for the +-J Ising spin glass model are theoretically shown based on a conjecture. 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