  We study the finite temperature properties of the extended Bose-Hubbard model
on a cubic lattice. This model exhibits the so-called supersolid state. To
start with, we investigate ordering processes by quantum Monte Carlo
simulations, and find successive superfluid and solid phase transitions. There,
we find that the two order parameters compete with each other. We obtain the
finite temperature phase diagram, which contains the superfluid, the solid, the
supersolid and the disordered phase. We develop a mean-field theory to analyze
the ordering processes and compare the result with that obtained by
simulations, and discuss the mechanism of the competition of these two orders.
We also study how the supersolid region shrinks as the on-site repulsion
becomes strong.

Statistical Mechanics