$ζ$-Pade SRWS theory with lowest order approximation

Abstract

In my previous preprint about SRWS-ζ theory[Y. Ueoka,viXra:2205.014,2022, I proposed an approximation of rough averaged summation of typical critical Green function for the Anderson transition in the Orthogonal class. In this paper, I remove a rough approximate summation for the series of the typical critical Green function by replacing summation with integral. Padé approximant is used to take a summation. The perturbation series of the critical exponent ν of localization length from upper critical dimension is obtained. The dimensional dependence of the critical exponent is again directly related with Riemann ζ function. Degree of freedom about lower critical exponent improve estimate compared with previous studies. When I fix lower critical dimension equal to two, I obtained similar estimate of the critical exponent compared with fitting curve estimate of the critical exponent [E.Tarquini et al.,PhysRevB.95(2017)094204].