{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"77c1b4b75bda5480bd555130965aba464f0e077b3104f4e17c0fd39b510d7a89","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["ab32b3f7a386733e616b0caf3f270e449f2e56b7ea17a78177cd8d74dbf321a2","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"40ef9cc428b4d3bd84a570f67740a0b7363757eee120f6c51533ef508397f5ee","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":["ai:gpt-5.5"],"external_id":"stat.kpz-higher-d.exponents-2plus1","kind":"well-posed","literature_status":"open","n":"2","parents":[],"plain":"For a growing two-dimensional surface, height fluctuations grow with system size as a power law with exponent $\\alpha$. Simulations give $\\alpha$ near 0.39, but no theory derives it.","posed_since":"1986","precise":"For the KPZ equation $dh/dt = \\nu \\mathrm{lap}\\ h + (\\lambda/2)(\\mathrm{grad}\\ h)^2 + \\eta(x,t)$ with Gaussian white noise $\\eta$ in $d = 2$ spatial dimensions, determine the roughness exponent $\\alpha$ (with $z = 2 - \\alpha$ from Galilean invariance) exactly or to $10^{-4}$, and decide whether it is a simple rational number. Large simulations give $\\alpha$ approximately 0.387 to 0.39; the conjecture $\\alpha = 2/5$ is disfavored.","problem_ref":"ab32b3f7a386733e616b0caf3f270e449f2e56b7ea17a78177cd8d74dbf321a2","references":"","settled_by":"An exact solution, or a nonperturbative RG computation with controlled error, agreeing with simulations to $10^{-4}$.","status_note":"","title":"Exact roughness exponent of KPZ surfaces in 2+1 dimensions","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"39dd15798939eba342de12958003685858d38452e633a5a7f5bbb5be9e060e9c","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"48299ac743e55df9caa183665a01bda20d954a4bd463eecfb0d920d993058621","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"RwUyRhx53I-gskE_zJQVsXcvBXoRGCddgwx_h7_pIs5vzgiNmQcK6X_sthU-2-JhOPkb6YR73llbQwIqNnxoCQ"},"schema":"pubphys.envelope/1"},"record_hash":"39dd15798939eba342de12958003685858d38452e633a5a7f5bbb5be9e060e9c","leaf_index":3786}