Critical Exponent of the Localization Length for the Symplectic Case

TL;DR

This paper introduces a new summability method to accurately calculate the critical exponent of localization length in the symplectic case, successfully resumming series in two dimensions and confirming theoretical bounds.

Contribution

It presents a novel summability technique that enables resummation of series in 2D, providing precise estimates of the critical exponent for the symplectic case.

Findings

Resummation in 2D yields $ u \\sim 1$

Values in $2+\\varepsilon$ dimensions saturate Harris inequality

Method improves accuracy over previous approaches

Abstract

A new summability method was tested to calculate the critical exponent $\nu$ of the localization length for the symplectic case derived from the non-linear $\sigma$-model. Although we used the same series as Hikami and others, unlike them we were able to resum the series in two-dimensions (2D) and obtain the result $\nu\sim 1$. Values of $\nu$ in $2+\varepsilon$ dimensions seem to saturate the Harris inequality up to $\varepsilon=0.2$.