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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 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