Nonuniversal effects due to leading effective-range corrections are computed for the ground-state energy of the weakly-coupled repulsive Bose gas in two spatial dimensions. Using an effective field theory of contact interactions, these corrections are computed first by considering fluctuations around the mean-field free energy of a system of interacting bosons. This result is then confirmed by an exact calculation in which the energy of a finite number of bosons interacting in a square with period boundary conditions is computed and the thermodynamic limit is explicitly taken.
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