  We study the transverse field Ising model on a kagome and a triangular
lattice using high-order series expansions about the high-field limit. For the
triangular lattice our results confirm a second-order quantum phase transition
in the 3d XY universality class. Our findings for the kagome lattice indicate a
notable instance of a disorder by disorder scenario in two dimensions. The
latter follows from a combined analysis of the elementary gap in the high- and
low-field limit which is shown to stay finite for all fields h. Furthermore,
the lowest one-particle dispersion for the kagome lattice is extremely flat
acquiring a dispersion only from order eight in the 1/h limit. This behaviour
can be traced back to the existence of local modes and their breakdown which is
understood intuitively via the linked cluster expansion.
