{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"10fd4828b85910b5b975ea7f6e7122fd938a98171ca5f7ba4b8a1144eda568f7","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"6ada2f4def7cc2d5a97125f7cec6186c8ebb1e8e8a40e4edc1ab3ba6dba3f197","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"stat.synchronization-networks.oscillator-glass","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"If oscillators are coupled with random signs, like spins in a spin glass, they may freeze into a disordered locked pattern, an oscillator glass. A peculiar transition seen in simulations in 1992 suggested this, but whether a true glass phase exists is unknown.","posed_since":"1992","precise":"For dtheta_i/dt = $\\omega_i$ + sum_j $J_{ij}$ sin(theta_j - theta_i) with Gaussian omega_i of unit variance and symmetric Gaussian couplings J_ij of variance $J^2/N$ (the Daido model), determine whether for $J$ above some $J_g$ the $N \\to \\infty$ dynamics has a frozen component, for example a nonzero limit of $C(\\tau) = (1/2N) \\operatorname{sum}_i \\langle \\cos(\\theta_i(t+\\tau) - \\theta_i(t))\\rangle$ as $\\tau \\to \\infty$. The volcano transition near $J = 1.3$ (a change in shape of the local-field distribution) is established; its relation to a glass phase is the question. Answer: yes or no, with $J_g$.","problem_ref":null,"references":"","settled_by":"A dynamical mean-field (cavity) solution at large J showing presence or absence of a persistent correlation plateau, confirmed by large-N simulations.","status_note":"A 2024 dynamical-cavity analysis explained the volcano transition and found no persistent correlation in the accessible range, arguing it does not imply a glass (arXiv:2310.09079).","title":"Existence of an oscillator glass in randomly coupled phase oscillators","topic_ref":"e69da0d5ffbbc9da951a478d590c05a19d606b183df93f87687dfb38b6e26853"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"b5386c02fad8d1191392bb60f49da2f511c4026165fe493120529009c3a0912a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"c48ff900c2cddb2249a5c7fa905bda900bb03b0a771dd48f1d768c6ecedc13ae","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"x0Wfk5FV1cu6iwBU3rkLyLJC2ofLWBtRmJyPsIAUQoyXWeRKq3zVVtTzxn3azFG16qwatjdXjP5CqWXnky4hAQ"},"schema":"pubphys.envelope/1"},"record_hash":"b5386c02fad8d1191392bb60f49da2f511c4026165fe493120529009c3a0912a","leaf_index":2122}