Additional numerical and graphical evidence to support some Conjectures on discrete Schrödinger operators with a more general long range condition

Abstract

This document contains additional numerical and graphical evidence to support some of the conjectures mentioned in \cite{GM3}. We give more evidence for $\kappa =3,4$ in dimension 2. As mentioned in that article we still don't quite understand the sets ${\mathbf{\mu }}_{\kappa }(\Delta )$ and ${\mathbf{\Theta }}_{\kappa }(\Delta )$ on $(0,1/2)$ for $\kappa =3$ in dimension 2. Here we give a bunch more threshold energies for $\kappa =3$ in dimension 2.