  We show that the critical point of the two-dimensional Bose-Hubbard model can
be easily found through studies of either on-site atom number fluctuations or
the nearest-neighbor two-point correlation function (the expectation value of
the tunnelling operator). Our strategy to locate the critical point is based on
the observation that the derivatives of these observables with respect to the
parameter that drives the superfluid-Mott insulator transition are singular at
the critical point in the thermodynamic limit. Performing the quantum Monte
Carlo simulations of the two-dimensional Bose-Hubbard model, we show that this
technique leads to the accurate determination of the position of its critical
point. Our results can be easily extended to the three-dimensional Bose-Hubbard
model and different Hubbard-like models. They provide a simple
experimentally-relevant way of locating critical points in various cold atomic
lattice systems.
