{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"ac96da215001d415c77bad48ae97f4a3ecba23949e947fc923ccfb5da5ba6e20","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["2b4970642076c5035a9f9d453147369eaed9186a1eb896d684c9d5793ce192f4","5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"3c3073eb287a2a3b414ded259f2ca772e58a558784d3db81e5bfee26a6f9d81b","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"stat.spin-glass-finite-d.at-line-3d","kind":"well-posed","literature_status":"contested","n":"1","parents":[{"note":"","parent_revision":"2b4970642076c5035a9f9d453147369eaed9186a1eb896d684c9d5793ce192f4","relation":"special_case"}],"plain":"In the solvable infinite-range model a spin glass stays glassy in a magnetic field up to a critical line in the field-temperature plane, the de Almeida-Thouless (AT) line. Whether such a line exists in three dimensions is a direct test between the competing theories.","posed_since":"","precise":"For the 3D Ising spin glass in a uniform or random field $h$, determine whether a thermodynamic phase transition occurs at nonzero $h_{\\mathrm{AT}}(T)$ for $T < T_c$, signaled by a diverging replicon susceptibility and replicon correlation length. Answer: yes or no, and the line $h_{\\mathrm{AT}}(T)$ if yes.","problem_ref":null,"references":"","settled_by":"Finite-size scaling of the replicon correlation length in equilibrium simulations of the 3D model in a field, at sizes where curves for different L cross at a stable point, or a proof.","status_note":"A 2024 analysis argues the AT line vanishes below six dimensions (arXiv:2402.03711), while 2025 simulations in $d = 5$ (arXiv:2510.14446) and a 2026 preprint in $d = 3$ (arXiv:2601.19192) report evidence for it.","title":"Existence of a de Almeida-Thouless line in three 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