In a previous work [1], we presented evidence that there is an Anderson transition below two dimensions in the symplectic universality class. Recently, this problem is the subject of renewed attention [2]. In a previous work [3], we have shown that the estimates of the critical exponent obtained in the non-linear sigma model formulation of the localisation problem are dramatically improved by incorporating in the Borel-Pade re-summation of the epsilon expansion for the critical exponent the asymptotic behaviour in high dimensions. In this paper [4], we will discuss the application of the Borel-Pade re-summation method directly to the beta functions of the Wigner-Dyson classes of the Anderson localisation problem. Examining the dimensionality dependence of the beta function allows us to estimate the lower critical dimension of the symplectic symmetry class.

[1] Y. Asada, K. Slevin, and T. Ohtsuki, Physical Review B 73, 041102 (2006).

[2] D. Sticlet and A. Akhmerov, Physical Review B 94, 161115 (2016).

[3] Y. Ueoka and K. Slevin, Journal of the Physical Society of Japan 83, 084711 (2014).

[4] Y. Ueoka. 2016. Some fundamental studies of critical phenomena of the Anderson transition in the Wigner-Dyson universality class. PhD thesis, Osaka University.