  We develop a strategy for calculating critical exponents for the Mott
insulator-to-superfluid transition shown by the Bose-Hubbard model. Our
approach is based on the field-theoretic concept of the effective potential,
which provides a natural extension of the Landau theory of phase transitions to
quantum critical phenomena. The coefficients of the Landau expansion of that
effective potential are obtained by high-order perturbation theory. We
counteract the divergency of the weak-coupling perturbation series by including
the seldom considered Landau coefficient $a_6$ into our analysis. Our
preliminary results indicate that the critical exponents for both the
condensate density and the superfluid density, as derived from the
two-dimensional Bose-Hubbard model, deviate by less than $1\%$ from the best
known estimates computed so far for the three-dimensional $XY$ universality
class.
