Borel-Padé re-summation of the ${\hat{I}}^2$-functions describing Anderson localisation in the Wigner-Dyson symmetry classes

Abstract

We describe a Borel-Padé re-summation of the ${\hat{I}}^2$-function in the three Wigner-Dyson symmetry classes. Using this approximate ${\hat{I}}^2$-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.