{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"dfc5cd6f2b73c51d9f0cd49afa3b0288f5d728199172de21b3fb21b9a4e8a3c2","created":"2026-10-03T07:17:58Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"ec0f7c939c462446cea3513bf519dcc1d4386dc9fc8bf1fbf1f17f0c3fca0bd5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"cm.anderson-transitions.interacting-3d-exponent","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"For electrons that do not repel, the transition exponent is known numerically to three digits. For real electrons, which repel through the Coulomb force, no reliable value exists.","posed_since":"","precise":"For 3D disordered electrons with $1/r$ repulsion (Finkelstein nonlinear sigma model; with and without spin-orbit scattering or magnetic field), compute the correlation-length exponent $\\nu$ and the dynamical exponent $z$ at the metal-insulator transition with controlled error, and compare with the non-interacting values $\\nu \\sim 1.57$ (orthogonal), $\\sim 1.44$ (unitary) and $\\sim 1.37$ (symplectic).","problem_ref":null,"references":"","settled_by":"A non-perturbative computation (self-consistent Hartree-Fock with exact diagonalization, functional renormalization group of the sigma model, or quantum Monte Carlo of a lattice model with Coulomb interaction) with finite-size scaling and error bars.","status_note":"A density-functional (Kohn-Sham, mean-field) model of a doped semiconductor gave $\\nu \\sim 1.3$ (Harashima and Slevin, Physical Review B 89, 205108, 2014), suggesting a different universality class; no controlled many-body result exists.","title":"Correlation-length exponent of the 3D Anderson-Mott transition with Coulomb interaction","topic_ref":"e7c62ae37eee99d87e4dd2b7fcb626097b84c27b343145bcc79a7fe68ba3dbb1"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d3010b8316b54191b345429dbb14ada06e292613204e1b7656e6faefc8efa8cb","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"6cfde648f8808ca657e645468603b96ae38c49705a26cd65df5161f9ba16b4b4","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ANsDFKlOG3M89RKnZ5RdTzP3RsZ4uoZPYRq4ib-ulGqreIXdQ_GPEcLSCI3CTZ1eQnMrqSE4Lwp0Q7EblEkDBA"},"schema":"pubphys.envelope/1"},"record_hash":"d3010b8316b54191b345429dbb14ada06e292613204e1b7656e6faefc8efa8cb","leaf_index":910}