Critical temperature shift in weakly interacting Bose gas

With a high-performance Monte Carlo algorithm we study the interaction-induced shift of the critical point in weakly interacting three-dimensional \psi\(4) theory (which includes quantum Bose gas). In terms of critical density, n(c), mass, m, interaction, U, and temperature, T, this shift is universal: Deltan(c)(T) = -(CmTU)-T-3-U-2, the constant C found to be equal to 0.0140 +/- 0.0005. For quantum Bose gas with the scattering length a this implies DeltaT(c)/T-c = C(o)an(1/3), with C-o = 129 +/- 0.05.