{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"bd8d0b1f544b7560f838d16271c421b997f4ff0fcd10cedbce435c1daeffff49","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"24f4f069fde06c7d89469f13232dd7ff9d97e81f945b7077038823b14b3aad1a","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"cm.mbl.heisenberg-chain-existence","kind":"well-posed","literature_status":"contested","n":"1","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":null,"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":"7f4724a8f5124a8d3b0876fec78a4f3f0f7b467672032acb318713bcededaa82"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"0cf86e50dcb1aedcccd0a8b2603b2d6cd8ba2dc41887681e77ef1284e7e962fe","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"a5449cda8b2a6261af7ced6332c4c1ed1ebf48fe90acf3a22819d4fb6fec0f71","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"WbEL_BRp1tsLBbR-lHmyH6RZwbQ0F16CD9cDSWgeKK_iKuSrJ5u0nfoCP_lfUwKAfdSY-eXX-7C1evvwMqB3Cw"},"schema":"pubphys.envelope/1"},"record_hash":"0cf86e50dcb1aedcccd0a8b2603b2d6cd8ba2dc41887681e77ef1284e7e962fe","leaf_index":1085}