{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"01c6e638e3502740f9dcc0c10958dd96964427b64a63c99b5d91e33aed8123e4","created":"2026-10-03T07:18:00Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["0cf86e50dcb1aedcccd0a8b2603b2d6cd8ba2dc41887681e77ef1284e7e962fe","5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"eb3814b4ee626e9244e1665e4a224e4ac08a711b69c1cec8d62d6ba48da83c81","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.mbl.critical-disorder-value","kind":"well-posed","literature_status":"open","n":"1","parents":[{"note":"","parent_revision":"0cf86e50dcb1aedcccd0a8b2603b2d6cd8ba2dc41887681e77ef1284e7e962fe","relation":"special_case"}],"plain":"If localization does occur above some disorder strength, the transition point and how quantities behave near it are unknown. Small-computer studies disagree with theories built on rare thermal patches.","posed_since":"","precise":"Assuming $W_{c}$ exists for the random-field Heisenberg chain, determine $W_{c}/J$ and the scaling near the transition (Kosterlitz-Thouless-like versus a finite correlation-length exponent $\\nu$, subject to the Harris-Chayes bound $\\nu \\ge 2$ in $d = 1$). Answer: $W_{c}$ with uncertainty and the scaling form of the characteristic length near $W_{c}$.","problem_ref":null,"references":"","settled_by":"Avalanche-stability numerics (chain coupled to an ideal bath at one end) extrapolated with a controlled scaling theory and consistent with renormalization-group predictions.","status_note":"","title":"Critical disorder and universality class of the MBL transition","topic_ref":"7f4724a8f5124a8d3b0876fec78a4f3f0f7b467672032acb318713bcededaa82"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"1fd0a5c63673313087b719e19eecc62b1063c5cb4edede620fa06ae733fb42c7","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"aa351a7f99ca7e5bd4c2ee47b1b7e923f483f9d4e7541aa9f518f6584419dab2","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"lsXSm_8GCJNgMZ5OiF0pIWmABl0p3nuqnwzWw7ipX9IlOXDM2wUvplLLZglVOKouqvXsAvgYUxEFXYuvYPazDw"},"schema":"pubphys.envelope/1"},"record_hash":"1fd0a5c63673313087b719e19eecc62b1063c5cb4edede620fa06ae733fb42c7","leaf_index":1086}