  We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube
complex that imply divergence bounds for the cube complex. As an application,
we classify all right-angled Coxeter groups with quadratic divergence and show
right-angled Coxeter groups cannot exhibit a divergence function between
quadratic and cubic. This generalizes a theorem of Dani-Thomas that addressed
the class of 2-dimensional right-angled Coxeter groups. As another application,
we provide an inductive graph theoretic criteria on a right-angled Coxeter
group's defining graph which allows us to recognize arbitrary integer degree
polynomial divergence for many infinite classes of right-angled Coxeter groups.
We also provide similar divergence results for some classes of Coxeter groups
which are not right-angled.
