{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"a5b1cb473eec5f263e538eefe74d8146c02c871717b3c80f7ce288d609dd3797","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"fe97cf2ac892d47d7296367381914f1adade2e1f2778ab9cf5e104a49e3e4983","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.kpz-higher-d.roughening-transition-d3","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Above two dimensions a KPZ surface stays smooth when the slope effect is weak and becomes rough when it is strong. A 2021 proposal says the transition point between the two lacks ordinary scale invariance and instead repeats its pattern only at discrete zoom factors.","posed_since":"2021","precise":"For the KPZ equation in $d = 3$ at the critical coupling $g_c$ separating the smooth (Edwards-Wilkinson) phase from the rough phase, equivalently the weak-to-strong disorder transition of directed polymers in $3+1$ dimensions, determine whether the transition is a scale-invariant fixed point (perturbative RG gives $z = 2$ and $\\alpha = 0$ there) or shows discrete scale invariance with log-periodic corrections, produced by a relevant three-body coupling of Efimov type (three-boson binding with a geometric spectrum) through the mapping to attractive bosons at their binding transition. An answer is a classification, with the log-periodic period if present.","problem_ref":null,"references":"","settled_by":"Simulations of directed polymers or growth models in $d = 3$ at the transition precise enough to detect or exclude log-periodic oscillations in free-energy or height fluctuations, or an RG computation that includes three-body operators.","status_note":"Nakayama and Nishida proposed Efimov-type discrete scale invariance at the transition (Phys. Rev. E 103, 012117, 2021, arXiv:2010.15161); no numerical test of it has been located.","title":"Scale invariance at the KPZ roughening transition in three 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