Critical Exponent of the Localization Length for the Symplectic Case

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 $\varepsilon=0.2$.