Transition temperature of the homogeneous, weakly interacting Bose gas

We present a Monte Carlo calculation for up to N similar to 20 000 bosons in 3D to determine the shift of the transition temperature due to small interactions a. We generate independent configurations of the ideal gas. At finite N, the superfluid density changes by a certain correlation function in the limit a --> 0; the N --> infinity limit is taken afterwards. We argue that our result is independent of the order of limits. Detailed knowledge of the noninteracting system for finite N allows us to avoid finite-size scaling assumptions.