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Proving this formula would confirm asymptotic freedom in a lattice model.","posed_since":"","precise":"For the $O(N)$ model on $Z^2$ with $N \\ge 3$, prove $\\xi(\\beta) = C_N \\beta^{-1/(N-2)} \\exp(2 \\pi \\beta/(N-2)) (1 + o(1))$ as $\\beta \\to \\infty$, with $\\xi = 1/m$ the exponential correlation length; the constant $C_N$ was predicted by Hasenfratz, Maggiore and Niedermayer (1990) from the Bethe ansatz. Answer: a proof of the leading asymptotics, with or without the constant.","problem_ref":"7c36ab60ff9ac3ebbc1ae5dceabeefa377c3a0741478e6a71fe3258e7b346b83","references":"","settled_by":"Matching upper and lower bounds on $\\xi(\\beta)$ with the two-loop exponential and power-law factors.","status_note":"","title":"Asymptotic-freedom growth of the O(N) correlation 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