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We describe a Borel-Pad\'e re-summation of the $\beta$-function in the threeWigner-Dyson symmetry classes. Using this approximate $\beta$-function wediscuss the dimensional dependence of the critical exponent and compare withnumerical estimates. We also estimate the lower critical dimension of thesymplectic symmetry class.

Borel-Pad\'e re-summation of the $\beta$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes