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 ΔTC/T₀~(na³)^γ, where γ0ex0ex=0ex0ex0.34±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.