Scaling function $\tau\to 0$ asymptotics of the correlation function in the $O_n-\varphi^4$ model

The results are given of a three-loop calculation of the scaling function $\tau\to 0$ asymptotics of the correlation function of the $O_n-(\varphi^4)_{4-\varepsilon}$ model to accuracy $\tau^{2+O(\varepsilon)}$.