  The ground-state properties of spin-polarized tritium T$\downarrow$ at zero
temperature are obtained by means of diffusion Monte Carlo calculations. Using
an accurate {\em ab initio} T$\downarrow$-T$\downarrow$ interatomic potential
we have studied its liquid phase, from the spinodal point until densities above
its freezing point. The equilibrium density of the liquid is significantly
higher and the equilibrium energy of $-3.664(6)$ K significantly lower than in
previous approximate descriptions. The solid phase has also been studied for
three lattices up to high pressures, and we find that hcp lattice is slightly
preferred. The liquid-solid phase transition has been determined using the
double-tangent Maxwell construction; at zero temperature, bulk tritium freezes
at a pressure of $P=9(1)$ bar.

Statistical Mechanics;Other Condensed Matter