{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"e8bcb32a2dd85e6eeaa34af476a5c22929e145d6f5aae826929f0038f8ea3c24","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"f94c507f018d7cf97d8917a848837422c1ccbabfcafee7253d87983c156dbb12","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"identification","assisted_by":[],"external_id":"stat.ising-3d.closed-form-solution","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Can the free energy of the 3D Ising model, or at least its critical exponents, be written as an exact formula? Numerics and the conformal bootstrap (a method that constrains critical points from symmetry and consistency) give the exponents to six or more digits, but no formula is known.","posed_since":"1944","precise":"For the nearest-neighbor Ising model on the simple cubic lattice, find a closed-form expression for the free energy per site, or for the universal exponents $\\nu = 0.629971(4)$ and $\\eta = 0.0362978(20)$ (conformal bootstrap values), or show that none exists within a stated class of closed forms. Computing Ising partition functions on general nonplanar graphs with arbitrary couplings is NP-hard (Istrail 2000), but this does not exclude an exact solution for the uniform cubic lattice; none is known. The open part is whether the free energy or the universal exponents have a closed form.","problem_ref":null,"references":"","settled_by":"An exact derivation, for example from a hidden integrable structure, that reproduces the numerical exponents, or a proof that they lie outside a stated class of closed forms.","status_note":"","title":"Closed-form free energy or exponents of the 3D Ising model","topic_ref":"19afc80a045932b8aeafee2d78656bd6c97eb566258215dd3cc140a709804606"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b5387de5ebb8f57475b4d6ddb52e8674dd2cfb04430e9872a3ff42e303abf9d2","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"830526a71ddfd3f31e431c45e10924589fe5609f613db30426af07382f5bc807","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ePKiKyw9yW0CAT8x1Ht4y9Ru-RtwDZNFVa1Lgxg7TgPJFFmbZyZN7HKdbVM9TYqR4JeOavHU9ZQZK94dOoekDQ"},"schema":"pubphys.envelope/1"},"record_hash":"b5387de5ebb8f57475b4d6ddb52e8674dd2cfb04430e9872a3ff42e303abf9d2","leaf_index":2082}