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

Abstract

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 $\ensuremath{\Delta}{T}_{C}{/T}_{0}\ensuremath{\sim}({\mathrm{na}}^{3}{)}^{\ensuremath{\gamma}}$, where $\ensuremath{\gamma}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.34\ifmmode\pm\else\textpm\fi{}0.03$. 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.