{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"b36f1185f7a42875eae1b913e5a7c1cc40ee1f77e90f470459d585bd73e4092e","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"cd1dacef58e8898a4879d6f71de9a04bcd5f55ec77e940c70963b9db0a45585d","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"stat.mpemba-relaxation.critical-universality","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Near a phase transition (such as a magnet losing its magnetization at a critical temperature), relaxation becomes slow and governed by a few universal numbers. The question is whether the existence and timing of Mpemba effects there are also fixed by those universal numbers.","posed_since":"","precise":"Ising-class system with non-conserved order parameter (Glauber or model-A dynamics), bath temperature $T_{\\mathrm{b}}$ near the critical temperature $T_{\\mathrm{crit}}$, initial equilibrium at $T_{0}$. Using a stated distance from final equilibrium, determine whether the existence of direct $\\left(T_{0} > T_{\\mathrm{b}}\\right)$ and inverse $\\left(T_{0} < T_{\\mathrm{b}}\\right)$ Mpemba effects and the crossing time $t_{x}$ obey scaling forms $t_{x} \\sim \\left|T_{\\mathrm{b}} - T_{\\mathrm{crit}}\\right|^{-\\nu z} F\\left(\\left(T_{0} - T_{\\mathrm{crit}}\\right)/\\left(T_{\\mathrm{b}} - T_{\\mathrm{crit}}\\right)\\right)$ set by the static exponent $\\nu$, the dynamic exponent $z$ and the order of the transition, independent of lattice and microscopic rates. The answer is a classification of where each effect occurs, with the scaling function $F$ or a demonstration that none exists.","problem_ref":null,"references":"","settled_by":"Large-scale Monte Carlo or renormalization-group computation across several models of one universality class showing a common F and common boundaries for direct and inverse effects.","status_note":"A Landau theory predicts Mpemba effects at phase transitions (Holtzman and Raz 2022), and Monte Carlo work on Ising and Potts models reports a scaling picture, set by the initial-state correlation length, that holds across first- and second-order transitions (Chatterjee et al., arXiv:2309.03709); no scaling function $F$ in terms of $\\nu$ and $z$ with RG or multi-model confirmation has been established (2026).","title":"Universal scaling of direct and inverse Mpemba effects near criticality","topic_ref":"b9dc5bd92d3519c9f31327e4098f8e26bf4890131f68cb53d43d3834030d1d0c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"5755725e511243a3280279f58b4c7328c0b7390d5cf5913a50e970037511b009","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"210c21abfa88484e46df3ccac4733a76ae26a1e0f2ea33bb6fb2ce380d3461f4","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"XmM3gbRtGUc52q9ha9VpPW7mkLXl4RLAeywoShvH8iStJ11nQbmgqTK4lcpfzmfybI-kTic-lbPUnLcbJWGSCA"},"schema":"pubphys.envelope/1"},"record_hash":"5755725e511243a3280279f58b4c7328c0b7390d5cf5913a50e970037511b009","leaf_index":2100}