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Their numerical values are known very precisely, but even their existence is unproven.","posed_since":"","precise":"Nearest-neighbour Ising model on $Z^3$ at $\\beta_c$. Prove that $\\langle s_0 s_x\\rangle_{\\beta_c}=\\left|x\\right|^{-(1+\\eta)+o(1)}$ and that the correlation length $\\xi(\\beta)=(\\beta_c-\\beta)^{-\\nu+o(1)}$, with numerical values $\\eta\\ \\mathrm{approximately}\\ 0.0363$ and $\\nu\\ \\mathrm{approximately}\\ 0.6300$. Answer: a proof of existence of the limits, with or without their values.","problem_ref":"50d6ad4de94c1993ab57ccb384ce833fadf21149df71edec04349a9a7fe38b85","references":"","settled_by":"A proof that the exponents $\\eta$ and $\\nu$ exist as limits.","status_note":"Continuity of the phase transition in 3D was proven by Aizenman, Duminil-Copin and Sidoravicius (2015).","title":"Existence of critical exponents for the 3D Ising 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