We consider a three-dimensional weakly interacting Bose gas in the fluctuation region (and its vicinity) of the normal-superfluid phase transition point. We establish relations between basic thermodynamic functions: density, n(T, ì), superfluid density ns(T, ì), and condensate density, ncnd(T, ì). Being universal for all weakly interacting |ø|4 systems, these relations are obtained from Monte Carlo simulations of the classical |ø|4 model on a lattice. Comparing with the mean-field results yields a quantitative estimate of the fluctuation region size. Away from the fluctuation region, on the superfluid side, all the data perfectly agree with the predictions of the quasicondensate mean field theory.—This demonstrates that the only effect of the leading above-the-mean-field corrections in the condensate based treatments is to replace the condensate density with the quasicondensate one in all local thermodynamic relations. Surprisingly, we find that a significant fraction of the density profile of a loosely trapped atomic gas might correspond to the fluctuation region.
Prokof'ev, Nikolai; Ruebenacker, O; and Svistunov, Boris, "Weakly Interacting Bose Gas in the Vicinity of the Critical Point" (2004). Physics Department Faculty Publication Series. 1139.