{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"dd80e326b870f7082b4536b003d1c95b4b561bd747ac6d91e380098565f8602d","created":"2026-10-03T07:18:11Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"5f24089ce83c48610f9d621b800f6c9ed981aaee3d9f7d06a4be53625ca60f8f","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-near-six","kind":"well-posed","literature_status":"contested","n":"1","parents":[],"plain":"Above six dimensions spin-glass theory becomes simple and the field-driven transition certainly exists. One prediction says it disappears exactly as the dimension drops to six; if so, it cannot exist in three dimensions.","posed_since":"2011","precise":"For Ising spin glasses on d-dimensional hypercubic lattices, or one-dimensional chains with couplings $J_{ij} \\sim r_{ij}^{-\\sigma}$ that mimic dimension d, determine whether $h_{\\mathrm{AT}}(T)$ is nonzero at $d = 6$ and slightly below, testing the Moore-Bray prediction $h_{\\mathrm{AT}}^2/T_c^2 = C (d-6)^4 (1 - T/T_c)^{d/2-1}$ as $d \\to 6$ from above. Answer: yes or no for $d = 6$ and for d just below 6.","problem_ref":null,"references":"","settled_by":"Simulations of 6D lattices or long-range one-dimensional proxies with controlled finite-size scaling of the replicon susceptibility, or an RG computation that fixes the fate of the AT fixed point.","status_note":"Large simulations report a transition in a field in $d = 6$ (arXiv:2306.00569, 2023) and in $d = 5$ (arXiv:2510.14446, 2025), while long-range one-dimensional simulations find $h_{\\mathrm{AT}}^{2} \\sim (2/3 - \\sigma)$, vanishing at the proxy of $d = 6$ (arXiv:2402.03711, 2024), as predicted in 2011 (arXiv:1102.1675).","title":"Fate of the de Almeida-Thouless line as dimension approaches 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