{"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 six","topic_ref":"2fabbf2d62cd6cfeaad5bb54ef05b26854ae4b38a41f86b17737f97acef6a87f"},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"e78c65ae72b5e290ca629fb4f2cd27ffa764bfb062fbbb4e7e871d70388c55ee","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"62308025c6912e9e5793e6b7e169a339e13a0ad62cb6ffa101db8b1015140258","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"6CNRky81RNAjZhueRnulrifOnSJk18d3cyWh9jyXNVhjAj-CmUL6I2c6tmBdqILNuqxsF9CjEt5ZKFGsA_Z1AA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIYjCAJcaRLp5Xk-a34WmjOeE6CtYstv-hAduLEBUUAljwIGI2IaytTuvKZFnVcvcmbhVKwXrJrcnEr_AtefL789JOCPEgZyHuDVSPGHwssJPTWqt74uleDge1lp5JRbw8VVj2248I8CBsy1T8sL1i8be9TR1IPzeYrOZJpP_TkFsk0v-bQ4fNdQjwIK3vEFagoeK-NoOidhp9XPXCyQLSg5RKHrB7anE6kAdeCPEgyqmIc-CAL5l5SW4YZTqfjh3l-wqkYlkTyQd0orHkK_gI8CAxWaX02zG7IG5Hzsb5DvBD8s-TaCVLfSN9pPb4HJqPDAjxIDLuS2H5mkQT51okBzSqxvYOZ2DzeEjrKj1FhjpNDRblCPAgOatp97sEGfSkPectTIcXn_UGSclxLvXC9ouOsHYFkl8I8CBPLfD1TsHdjhkyZ9iTm9m5GTCSBT-7GhYUfap1vptsnQjxINBAKCf3cKChW811B6TkfdlxdONUiLQA88uJMnPer4KuCPEgytIBB3x7TFDT-XqOV-9vpqw1NKoAu0dhtsCbAMql2L0I8CCtNZgmApuKULvPC9nsMCaM05arV-F3o5FTlnJCnRvdMgjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvACD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEI8WC8CttjWJlWtU2tDxvRDBJXcN7BbcwWdRcPCgTYZZnwIPFz7fO-aP-QJQZ2ZKGm-LPdYK__xV33xZeJeSjGVoNyCPEgXP6-DxgrztrmqkB9N5lRPQxcCDBGxn1j3v4gUiUplScI8CDT7doL_ICPCgKR77kUy7nTfjemiZ1kyLcCMmeu_czvZQjwIEV-XA96d796v-7QBxpca4NGPkhP0Wf89ukLcXZ87vmICPEgGq_RwHEiOpQh2pT_WRHcCsyInKcc2JIvmb6SzmimiC0I8SBjwX1mn1v0lrKsqzDOtikQv9q6kVbAZnqd0E2evRTK-gjwIAz1dj1zoq3Q3xYVUK230VvgL9_uFVNS120UrX5BlfFcCPEgb1HWQLf7N5Rua2bORFDL2fDBJS7iVOSaHp7adL8jwH8I8SAVG4HLRiZRZ26g7AYBWDSI50GY2TGlNC7pHIYc-vQ3UgjxIOUdEg6sSGuGAwm6byKNwNSH-CaFtay_ppzVi8InqIsBCPEgUZCxxJx-baWw4JFRfzCCtSjPn4ATBx_3FQi1O2Yo4-8I8SAQuuTPkAGyvS_wKMy9BtKvnki2puESdY2vXem8hT1uIQjwIBGYo5Vxy-d7U5zKv5vp3Ii7hJPH_BDLCzA13c47p9q7CP_wCHbghVgOFMuNCPAQPZK2lHbTMqcCYUotzOQcmQjwIJ7ruRIs6HnufKxCpmLUgeUl0aUu0ov4_3PqcppS-bddCPEgI530vHzdwz_3o9jYQ3WablSaV64Wfn7Pmby5WLyI-A0I8QRqwKw78AhITF7Tr3a1xACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AIfrBm5kAMH2cI8BAGKsbR52Yj2ZyRBj8fybyrCPEg15Kg4Ne2LGSKxM-WnEce5gVwiluZijYEWJ8P_lNnKQ4I8QRqwKw68AhHyujKJ6ONvACD3-MNLvkMji4taHR0cHM6Ly9hbGljZS5idGMuY2FsZW5kYXIub3BlbnRpbWVzdGFtcHMub3Jn"]},"log":{"leaf_index":"2110","tree_size":"2123","proof":["045a71df21eb047bfd751f67e6548a03e15d5c1077bff4b9fe04c96646679f62","9bf8ddca1cedb22fbdb3ffe00bdf1e2c45263b2f554eb152ca8f7b80c4ebbe6e","56bde87580bc11bcff1c998a9189343ac30f31676602b965d7a401f876e74cca","bd083dc7529c5a1f40d40ba6cfc7973f9c775e8858b8c7e054dc5c04a3d019e4","3ae52a1c64216f4a40d333d886cd08e483cb70a3acba7bed03fbdd4acae14e72","599335fb93a39cc33020aebcb4210acc2ef94181f860c6c23a92e0f385723d93","e6fe28a74db11e411f7b825398eaff5c6a5c1228133acc9bc663eaf6ba57e637","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n2123\npXVcluz7BF4vgChQs6lShuU0386gCH0RxrC1sxyE3rI=\n\n— pubphys.com/log/v1 JFPwIOLzsUD22XoTVyTfk/FMVj/u3f3DxZk4V/Ws10KVSS+8WQSwhunQ//EAhyS9Td5CyM0E++85GMezmKd8240j9Q8=\n","promise":null},"orcid_key_evidence":[],"attesting":null}