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: $\Delta n_c\left(T\right){=-Cm}^3{T}^{2}U$, the constant $C$ found to be equal to $0.0140\pm 0.0005$. For quantum Bose gas with the scattering length $a$ this implies $\Delta T_c{/T}_c{=C}_0{\mathrm{an}}^{1/3}$, with $C_0=1.29\mathrm{}\pm 0.05$.