{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"77fbbddac305a94ab3ec9a37d2a6af6a4a7d0d09e0b7e33bad8a86016a1a7b91","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["0cf86e50dcb1aedcccd0a8b2603b2d6cd8ba2dc41887681e77ef1284e7e962fe","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"f3156b02b1cf9ee1137a8617ca62b45b3652b9c89a0c1bf8943ce88d192d94df","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"cm.mbl.heisenberg-chain-existence","kind":"well-posed","literature_status":"contested","n":"2","parents":[],"plain":"The standard test case is a chain of quantum spins in random magnetic fields of strength W. The question is whether, for large enough W, an infinitely long chain stays out of equilibrium forever.","posed_since":"2006","precise":"$H = \\sum_i J S_i . S_{i+1} + h_i S^{z}_i$ with $h_i$ independent and uniform in $[-W, W]$. Does a $W_c < \\infty$ exist such that for $W > W_c$ infinite-temperature eigenstates obey an area law and local memory of the initial state persists as $t \\to \\infty$, in the limit $L \\to \\infty$? Answer yes or no, with an estimate or bound on $W_c$.","problem_ref":"0cf86e50dcb1aedcccd0a8b2603b2d6cd8ba2dc41887681e77ef1284e7e962fe","references":"","settled_by":"A proof for this model (Imbrie's 2016 proof covers a random Ising chain with transverse field and relies on an unproven limited-level-attraction assumption), or numerics that control rare thermal regions at sizes where avalanche effects are visible.","status_note":"Avalanche studies (Morningstar et al. 2022, arXiv:2107.05642) place any transition at disorder well above the exact-diagonalization crossover W of about 4J; existence itself remains debated in 2025-2026.","title":"Is the random-field Heisenberg chain localized at strong disorder?","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8fe1ef633f569dfcfa803d6631c52d731f0bbbd857c3c9ce87dc14fdcea8f86c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"59d8b23a52d56187a48eac9ac2dc5372ad13f7a4d2967abd3b065d5ab379e4b9","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ii79vGbt0zByZwRN4iPu2n1X6EgB8EyIo7E-lrYpB0ZPL3XfMrye_5vJrVc339NmeSUrPMT0f4mSWsDCiSARBg"},"schema":"pubphys.envelope/1"},"record_hash":"8fe1ef633f569dfcfa803d6631c52d731f0bbbd857c3c9ce87dc14fdcea8f86c","leaf_index":2932}