{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"44862f11af63734af61f4ef369c6894f5e121ccec773788c5f6f8dea790f4fed","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"4bf7271387f4d51666ce520151f7e369f773048ce37d170a133f74867c06f54d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"mathph.ising-rigorous.nongaussian","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"In four or more dimensions the critical Ising model looks like a free (Gaussian) field at large scales. In 3D it should not, and this difference is unproven.","posed_since":"","precise":"Prove that every subsequential scaling limit of the critical spin field on $Z^{3}$ is non-Gaussian, for example that the rescaled fourth Ursell function does not vanish, and that $\\eta > 0$ strictly (the infrared bound gives only $\\eta \\ge 0$). Answer: a proof.","problem_ref":null,"references":"","settled_by":"A proof of a nonvanishing four-point Ursell function in the 3D scaling limit.","status_note":"Gaussianity is proven for $d \\ge 5$ (Aizenman; Frohlich, 1982) and $d = 4$ (Aizenman and Duminil-Copin, 2021).","title":"Non-Gaussian scaling limit of the critical 3D Ising model","topic_ref":"0b88a0ded9bd47630f1a876bef355f9b17efdebced19bd55e73bb1cd79f5cae3"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9550a3b10874cc87ea667035cf8b7b522b717c9e3e35c26652eac4cb15cf514b","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"839609af1020d24de7d05e0732bb88784edb8bd3ea3f394d10c8bb24a067a57e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"KrD2F8kIF4AvJF_-IkiRJXeD5JN160ZyAksIxCfKEkYPFrFmTHBbmepZDqoUp5ROXbqvnedFL2k4b0nSCz1xCQ"},"schema":"pubphys.envelope/1"},"record_hash":"9550a3b10874cc87ea667035cf8b7b522b717c9e3e35c26652eac4cb15cf514b","leaf_index":1631}