  We study the quantum phase transition from a super solid phase to a solid
phase of rho = 1/2 for the extended Bose-Hubbard model on the honeycomb lattice
using first principles Monte Carlo calculations. The motivation of our study is
to quantitatively understand the impact of theoretical input, in particular the
dynamical critical exponent z, in calculating the critical exponent nu. Hence
we have carried out four sets of simulations with beta = 2N^{1/2}, beta =
8N^{1/2}, beta = N/2, and beta = N/4, respectively. Here beta is the inverse
temperature and N is the numbers of lattice sites used in the simulations. By
applying data collapse to the observable superfluid density rho_{s2} in the
second spatial direction, we confirm that the transition is indeed governed by
the superfluid-insulator universality class. However we find it is subtle to
determine the precise location of the critical point. For example, while the
critical chemical potential (mu/V)_c occurs at (mu/V)_c = 2.3239(3) for the
data obtained using beta = 2N^{1/2}, the (mu/V)_c determined from the data
simulated with beta = N/2 is found to be (mu/V)_c = 2.3186(2). Further, while a
good data collapse for rho_{s2}N can be obtained with the data determined using
beta = N/4 in the simulations, a reasonable quality of data collapse for the
same observable calculated from another set of simulations with beta = 8N^{1/2}
can hardly be reached. Surprisingly, assuming z for this phase transition is
determined to be 2 first in a Monte Carlo calculation, then a high quality data
collapse for rho_{s2}N can be achieved for (mu/V)_c ~ 2.3184 and nu ~ 0.7 using
the data obtained with beta = 8N^{1/2}. Our results imply that one might need
to reconsider the established phase diagrams of some models if the accurate
location of the critical point is crucial in obtaining a conclusion.
