Borel-Pade Re-Summation Of The Beta-Functions Describing Anderson Localisation In The Wigner-Dyson Symmetry Classes

We describe a Borel-Pade re-summation of the beta-function in the three Wigner-Dyson symmetry classes. Using this approximate beta-function we discuss the dimensional dependence of the critical exponent and compare with numerical estimates. We also estimate the lower critical dimension of the symplectic symmetry class.