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

Abstract

We describe a Borel-Padé 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.

References in corpus (4)

• Anderson Transitions
• Dimensional dependence of the metal-insulator transition
• Finite-size scaling and multifractality at the Anderson transition for the three Wigner-Dyson symmetry classes in three dimensions
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes

Cited by in corpus (2)

• Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes