English

$\zeta$-Pade SRWS theory with lowest order approximation

Disordered Systems and Neural Networks 2022-10-18 v2

Abstract

In my previous paper about SRWS-ζ\zeta 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. Pade approximant is used to take a summation. The perturbation series of the critical exponent ν\nu of localization length from upper critical dimension is obtained. The dimensional dependence of the critical exponent is again directly related with Riemann ζ\zeta 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]. 1

Keywords

Cite

@article{arxiv.2210.01773,
  title  = {$\zeta$-Pade SRWS theory with lowest order approximation},
  author = {Yoshiki Ueoka},
  journal= {arXiv preprint arXiv:2210.01773},
  year   = {2022}
}

Comments

8pages, 2figures

R2 v1 2026-06-28T02:47:48.177Z