  We investigate systems of bosonic particles at zero temperature in triangular
and hexagonal optical lattice potentials in the framework of the Bose-Hubbard
model. Employing the process-chain approach, we obtain accurate values for the
boundaries between the Mott insulating phase and the superfluid phase. These
results can serve as reference data for both other approximation schemes and
upcoming experiments. Since arbitrary integer filling factors g are amenable to
our technique, we are able to monitor the behavior of the critical hopping
parameters with increasing filling. We also demonstrate that the g-dependence
of these exact parameters is described almost perfectly by a scaling relation
inferred from the mean-field approximation.
