  We establish the nature of the supersolid phase observed for hardcore bosons
on the triangular lattice near half-integer filling factor, and study the phase
diagram of the system at finite temperature. We find that the solid order is
always of the (2m,-m',-m') with m changing discontinuously from positive to
negative values at half-filling, contrary to predictions of other phases, based
on an analogy with the properties of Ising spins in transverse magnetic field.
At finite temperature we find two intersecting second-order transition lines,
one in the 3-state Potts universality class and the other of the
Kosterlitz-Thouless type.
