We study various properties of bosons in two dimensions interacting only viaonsite hardcore repulsion. In particular, we use the lattice spin-waveapproximation to calculate the ground state energy, the density, the condensatedensity and the superfluid density in terms of the chemical potential. We alsocalculate the excitation spectrum, $\omega({\bf k})$. In addition, we performedhigh precision numerical simulations using the stochastic series expansionalgorithm. We find that the spin-wave results describe extremely well thenumerical results over the {\it whole} density range $0\leq \rho \leq 1$. Wealso compare the lattice spin-wave results with continuum results obtained bysumming the ladder diagrams at low density. We find that for $\rho \leq 0.1$there is good agreement, and that the difference between the two methodsvanishes as $\rho^2$ for $\rho \to 0$. This offers the possibility of obtainingprecise continuum results by taking the continuum limit of the spin-waveresults for all densities. Finaly, we studied numerically the finitetemperature phase transition for the entire density range and compared with lowdensity predictions.
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