Weakly interacting Bose gas in the vicinity of the critical point

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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,μ), superfluid density nₛ(T,μ), and condensate density, n cnd (T,μ). Being universal for all weakly interacting |ψ|⁴ systems, these relations are obtained from Monte Carlo simulations of the classical |ψ|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.