{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6651fd65b40d7d73fb1c3f7cf2d77386730976bbfda57134a6265b10f317771d","created":"2026-10-03T07:18:10Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5cd7906a025aa2beb2e1d2084d26764885ca68c5bb667ebcae4c4642c7ebadfb","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"stat.ising-3d.dynamic-exponent-z","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Near the critical point a magnet relaxes very slowly, and the exponent z sets how the relaxation time grows with the size of correlated regions. For purely relaxational dynamics in three dimensions, z is known only approximately and has no exact theory.","posed_since":"","precise":"For relaxational (model A, e.g. Glauber or Metropolis) dynamics in the 3D Ising universality class, determine $z$ in $\\tau \\sim \\xi^z$ to precision $10^{-4}$ or better. The best Monte Carlo estimate is $z = 2.0245(15)$ from the improved Blume-Capel model (arXiv:1908.01702), and the five-loop $\\epsilon$ expansion gives $z = 2.0235(8)$ (arXiv:2111.04719).","problem_ref":null,"references":"","settled_by":"An independent high-precision Monte Carlo study or a dynamical bootstrap or RG computation reaching $10^{-4}$ accuracy with controlled corrections to scaling.","status_note":"Monte Carlo gives $z = 2.0245(15)$ (arXiv:1908.01702) and the five-loop epsilon expansion gives $z = 2.0235(8)$ (arXiv:2111.04719, 2021), consistent within errors; $z \\ge 2$ was proven for Glauber dynamics in 2025 (arXiv:2502.09908).","title":"Dynamic critical exponent z of the 3D Ising model","topic_ref":"19afc80a045932b8aeafee2d78656bd6c97eb566258215dd3cc140a709804606"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"2be08cd5e93c0ffc251f0277ce5f83b4d2a5241025165ae477c8627710e1809a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"28079d4e02481df0a9eb8dbd01a89347abfa99256e8fe926adc648a1f7431d54","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"7Auptk4yWRfkVa_pWLTd8tg3VshiKqxlBsDjEdbq2boYr4d40CsNbvmbdC-S8sMxa4952mu0J_jtHd_sc-OnBA"},"schema":"pubphys.envelope/1"},"record_hash":"2be08cd5e93c0ffc251f0277ce5f83b4d2a5241025165ae477c8627710e1809a","leaf_index":2083}