  Motivated by excellent comparisons of spin wave theory (SWT) with Quantum
Monte Carlo (QMC) calculations of non-interacting hardore bosons (Bernardet et
al.) and superlattices (Hen et al.), we develop an SWT for interacting hardcore
bosons on a d-dimensional cubic lattice at zero temperature and compare
thermodynamical properties with results of Stochastic Series Expansions (SSE):
there is good comparison between SWT and SSE results for the simple cubic
lattice at small repulsive strengths but differences arise between the results
of the two approaches for the square lattice at strong repulsions. The
boundaries of the three phases - Mott insulating (MI), superfluid (SF) and
N\'{e}el solid (NS) - can be readily estimated from calculations of particle
density, signalling either a first order (SF <--> NS) or second order
transition (MI <--> SF). Comparison is made with results of the Bethe ansatz in
one dimension and QMC in two dimensions.
