Critical Temperature of Bose-Einstein Condensation of Hard-Sphere Gases

We determine the critical temperature of a 3D homogeneous system of hard-sphere bosons by path-integral Monte Carlo simulations and finite-size scaling. In the low density limit, we find that the critical temperature is increased by the repulsive interactions, as $\Delta T_C{/T}_0\sim ({\mathrm{na}}^3{)}^{\gamma }$, where $\gamma =0.34\mathrm{}\pm 0.03$. At high densities the result for liquid helium, namely, a lower critical temperature than in the noninteracting case, is recovered. We give a microscopic explanation for the observed behavior.