  We consider the grand potential $\Omega$ of a two-dimensional weakly
interacting homogeneous Bose gas at zero temperature. Building on a
number-conserving Bogoliubov method for a lattice model in the grand canonical
ensemble, we calculate the next order term as compared to the Bogoliubov
prediction, in a systematic expansion of $\Omega$ in powers of the parameter
measuring the weakness of the interaction. Our prediction is in very good
agreement with recent Monte Carlo calculations.
