{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6a15e21ad91d6d2f2fb8e7d0f9d2ab3eeac4060b0f6a8a3bc6745aa046f94158","created":"2026-10-03T07:17:57Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ebaa90dd89d08a8749d5098da55b6056c5d9a8cdb6ea2ff1f0697ec420807871","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"bio.jamming-rigidity.gardner-finite-d","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Mean-field theory predicts that a glass compressed deep into its solid state undergoes a further transition, the Gardner transition, where each glassy state splits into many nearly equivalent sub-states. Whether this transition survives in real three-dimensional glasses or is only a smooth crossover is unknown.","posed_since":"2014","precise":"In the $d \\to \\infty$ solution for hard spheres, a stable glass becomes marginally stable at a pressure $p_G$ through full replica symmetry breaking (a hierarchy of sub-basins). For $d = 3$ hard- or soft-sphere glasses, determine whether the caging susceptibility $\\chi_{AB}$ (fluctuation of the mean-square distance between two copies of the same glass) diverges in the thermodynamic limit at finite $p_G$, or stays finite. Perturbative arguments suggest the transition may be destroyed below $d = 6$, while a nonperturbative fixed point found in $d < 6$ would allow it.","problem_ref":null,"references":"","settled_by":"Finite-size scaling of $\\chi_{AB}$ in well-equilibrated $d = 3$ glasses showing divergence or saturation, or a renormalization-group proof of existence or absence.","status_note":"Simulations in $d = 2 \\text{ and } 3$ report Gardner-like crossovers (2016-2023), including a generic dynamic Gardner crossover in compressed hard disks (Liao et al., PNAS 2023); field theory is split between absence of the transition below $d = 6$ and a nonperturbative fixed point that would permit it.","title":"Does a true Gardner transition exist in three-dimensional glasses","topic_ref":"e88cb77371bb7a86f0fbdb1f952ba3eab78bc8141039cb805db532ac7cced95b"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"94d3280305428cfa8d5d0dbda4edd28da33099d579a573e80fe87bd7be3f4765","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"ea41b47d1e42fe4727676317dbd462baf90057222d8e4fa66edd9a290f3bc854","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"37Eq-02iQIwV-4i1CT-Cl1dmXG9xrXO6YvgnSRXYTborVkiOKb5Wf1dqPVglutI54Sqbztmmf6NAsF48x1NzCg"},"schema":"pubphys.envelope/1"},"record_hash":"94d3280305428cfa8d5d0dbda4edd28da33099d579a573e80fe87bd7be3f4765","leaf_index":788}